http://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&feed=atom&action=historyAbout pages for SOCR Experiments - Revision history2024-03-19T05:22:21ZRevision history for this page on the wikiMediaWiki 1.15.1http://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=7772&oldid=prevIvoDinov at 22:20, 5 July 20082008-07-05T22:20:36Z<p></p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* Here are some [[SOCR_Videos_Experiments | Experiments Video Tutorials]]</ins></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=2618&oldid=prevIvoDinov at 18:54, 29 January 20072007-01-29T18:54:40Z<p></p>
<a href="http://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=2618&oldid=2614">Show changes</a>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=2614&oldid=prevIvoDinov at 04:59, 23 January 20072007-01-23T04:59:06Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><p class="MsoNormal"> Demonstration of Central Limit Theorem (CLT).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><p class="MsoNormal"> Demonstration of Central Limit Theorem (CLT). <ins class="diffchange diffchange-inline">See the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | SOCR General Central Limit Theorem Experiment Activity]]</ins></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=2589&oldid=prevIvoDinov at 20:29, 22 January 20072007-01-22T20:29:02Z<p></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">class="SpellE"><b>Sampling Distribution CLT Experiment</b></span><b>:</b></p></del></div></td><td colspan="2"> </td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">style="">To view this experiment, click </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">and select “<span class="SpellE">Sampling Distribution CLT Experiment</span>” from the</del></div></td><td colspan="2"> </td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"><p class="MsoNormal"> This applet is part of the SOCR Experiments: Sampling Distribution (CLT) Experiment, which demonstrates the properties of the sampling distributions of various sample statistics. This applet can be used to demonstrate the Central Limit Theorem (CLT) as well as:<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">1. Investigate the effect of the Native population on various sample statistics; <br> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">2. Study the effects of the sample-sizes on the sampling distribution;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">3. Determine which sample statistics may have known distributions (e.g., Normal), under what conditions;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">4. Explore the relations between Population parameters and their corresponding sample counterparts;<br></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">For example population mean/SD and sample mean/SD, symmetry, distribution shape, etc.</del></div></td><td colspan="2"> </td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><p class="MsoNormal" style="text-align: center;" align="center"><span</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">class="SpellE"><b>Sampling Distribution CLT Experiment</b></span><b>:</b></p></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><p class="MsoNormal" style="text-align: center;" align="center"><span</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">style="">To view this experiment, click </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">and select “<span class="SpellE">Sampling Distribution CLT Experiment</span>” from the</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">list.<span style="">&nbsp; </span></span></p></ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><p class="MsoNormal"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">This applet is part of the SOCR Experiments: Sampling Distribution (CLT) Experiment, which demonstrates the properties of the sampling distributions of various sample statistics. This applet can be used to demonstrate the Central Limit Theorem (CLT) as well as:<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">1. Investigate the effect of the Native population on various sample statistics; <br> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">2. Study the effects of the sample-sizes on the sampling distribution;<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">3. Determine which sample statistics may have known distributions (e.g., Normal), under what conditions;<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">4. Explore the relations between Population parameters and their corresponding sample counterparts;<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">For example population mean/SD and sample mean/SD, symmetry, distribution shape, etc.</ins></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=2588&oldid=prevIvoDinov at 20:25, 22 January 20072007-01-22T20:25:45Z<p></p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">class="SpellE"><b>Sampling Distribution CLT Experiment</b></span><b>:</b></p></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><p class="MsoNormal" style="text-align: center;" align="center"><span</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">style="">To view this experiment, click </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">and select “<span class="SpellE">Sampling Distribution CLT Experiment</span>” from the</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">list.<span style="">&nbsp; </span></span></p></ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><p class="MsoNormal"> This applet is part of the SOCR Experiments: Sampling Distribution (CLT) Experiment, which demonstrates the properties of the sampling distributions of various sample statistics. This applet can be used to demonstrate the Central Limit Theorem (CLT) as well as:<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">1. Investigate the effect of the Native population on various sample statistics; <br> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">2. Study the effects of the sample-sizes on the sampling distribution;<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">3. Determine which sample statistics may have known distributions (e.g., Normal), under what conditions;<br></ins></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=1862&oldid=prevJenny at 19:44, 17 August 20062006-08-17T19:44:14Z<p></p>
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</table>Jennyhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=1714&oldid=prevIvoDinov at 18:01, 26 July 20062006-07-26T18:01:00Z<p></p>
<a href="http://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=1714&oldid=1713">Show changes</a>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=1713&oldid=prevIvoDinov at 17:17, 26 July 20062006-07-26T17:17:15Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>EXPERIMENTS</u></p></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>EXPERIMENTS</u></p></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=1712&oldid=prevIvoDinov at 17:15, 26 July 20062006-07-26T17:15:46Z<p></p>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=About_pages_for_SOCR_Experiments&diff=1711&oldid=prevIvoDinov at 16:49, 26 July 20062006-07-26T16:49:29Z<p></p>
<p><b>New page</b></p><div><table class="MsoNormalTable" style="width: 100%;" border="1"<br />
cellpadding="0"><br />
<tr style=""><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle; width: 25%;"><br />
<p class="MsoNormal"<br />
style="margin-bottom: 12pt; text-align: center;" align="center"><u><br><br />
EXPERIMENTS</u></p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal"><u><br><br />
</u></p><br />
<div style="text-align: center;"><u>DESCRIPTION</u></div><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal"><u><br><br />
APPLICATIONS</u></p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>Ball<br />
and Urn Experiment</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “Ball and Urn Experiment” from the list.<span style="">&nbsp;<br />
</span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This experiment exemplifies the<br />
binomial distribution.&nbsp; The user determines the parameters of the<br />
binomial distribution (<span class="SpellE"><b style="">n<span<br />
class="GramE">,p,k</span></b></span>), and the computer randomly<br />
choose balls according to that distribution.&nbsp; The red ball is<br />
considered a “success”, while the green ball is considered the<br />
“failure”.&nbsp; The blue histogram displays the probabilities of<br />
choosing all possible numbers of red balls, while the red histogram<br />
displays the observed proportions of the cumulative number of red balls<br />
chosen per trial.&nbsp; The theoretical and observed μ and σ are<br />
displayed beneath the histograms.&nbsp; The numerical probabilities and<br />
observed proportions of each result are also given.&nbsp; </p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">Binomial Distribution</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BallotExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BallotExperiment</span>:<b></b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b<br />
style="">&nbsp;</b></p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">In an election, candidate A receives <span<br />
style="font-weight: bold;">a</span> votes and candidate B receives <span<br />
style="font-weight: bold;">b</span> votes, where <b>a &gt; b</b>. The<br />
votes are assumed to be randomly ordered. The first graph shows the<br />
difference between the number of votes for A and the <span<br />
class="GramE">number of votes for B, as the votes are</span> counted. <b>The<br />
event of interest is that A is always ahead of B in the vote count, or<br />
equivalently, that the graph is always above the horizontal axis</b><br />
(except of course at the origin). The <i>indicator variable I of this<br />
event is recorded in the first table</i> on each update. The density<br />
function of I is shown in blue in the second graph and is recorded in<br />
the second table. On each update, the empirical density of I is shown<br />
as red in the second graph and recorded in the second table. The<br />
parameters <span class="GramE"><span style="font-weight: bold;">a</span><br />
and</span> <span style="font-weight: bold;">b</span> can be varied<br />
with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BertrandExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BertrandExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">Bertrand's experiment is to generate a<br />
random chord of a circle. In the <span class="SpellE">simulation, one</span><br />
point of the chord is fixed at (1, 0) and the other random point (X, Y)<br />
is recorded on each update in the first table. Also recorded are <u>D,<br />
the length of the line <span class="SpellE">segment from</span> the<br />
center of the circle to the center of the chord</u>, and <u>A, the<br />
angle that this <span class="SpellE">line segment</span> makes with<br />
the horizontal</u>. Variable <b><i style="">I</i> <span class="GramE">indicates</span><br />
the event that the chord is longer than the length of a side of the<br />
inscribed equilateral triangle</b>. The density of I is shown in blue<br />
in the distribution graph and <span class="SpellE">and</span> is<br />
recorded in the distribution table. On each update, the empirical<br />
density of I is shown in red in the distribution graph and is recorded<br />
in the distribution table. Three different models can be selected with<br />
the list box: the model where the distance D is uniformly distributed,<br />
the model where the angle A is uniformly distributed, and the model<br />
where the coordinate X is uniformly distributed.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BetaCoinExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BetaCoinExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to toss <span<br />
class="GramE">a coin n times</span>, where the probability of heads is<br />
p. The <b>probability of heads is modeled with a prior </b><b style=""><i<br />
style="">β</i></b><i style=""> <b>distribution</b></i>, having<br />
parameters <span class="GramE"><b><i style="">a</i> </b>and</span> <b><i<br />
style="">b</i></b>. The prior density and the true probability of<br />
heads are shown in blue in the graph on the right. On each update, the<br />
number of heads Y is recorded in the first table. On each update, the <b>posterior<br />
</b>β <b>density, which has parameters a + Y and b + n - Y is<br />
shown in <span style="color: rgb(255, 102, 0);">red</span> in graph on<br />
the right</b>. Also, the <b>Bayesian estimate of p, U = (a + Y) / (a +<br />
b + n)</b> is recorded in the first table on each update. Finally, the<br />
second table gives the true <span class="SpellE">distBias</span> and<br />
mean square error of <span class="GramE">U,</span> and on each update<br />
gives the empirical <span class="SpellE">distBias</span> and mean<br />
square error, based on the all of the runs of the experiment. The<br />
parameters <b style=""><i style="">n, p, a,</i> </b>and<b style=""> <i<br />
style="">b</i></b> can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Bayesian Estimation - Prior/Posterior.</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BetaEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BetaEstimateExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
is to generate a random sample X<sub>1</sub>, X<sub>2</sub>, ..., <span<br />
class="SpellE">X</span><sub>n</sub> of size n from the <b style="">β <span<br />
style="">distribution with parameters a and 1</span></b>. The<br />
distribution density is shown in blue in the graph, and on each update,<br />
the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. On each update, the<br />
following statistics are recorded: </p><br />
<p style="text-align: center;" class="MsoNormal">U<br />
= M / (1 - M) where M = (X<sub>1</sub> + X<sub>2</sub> + ••• + <span<br />
class="SpellE">X</span><sub>n</sub>) / n<br><br />
V = -n / [<span class="SpellE">ln</span>(X<sub>1</sub>) + <span<br />
class="SpellE">ln</span>(X<sub>2</sub>) + ••• + <span class="SpellE"><span<br />
class="GramE">ln</span></span><span class="GramE">(</span><span<br />
class="SpellE">X</span><sub>n</sub>)]. </p><br />
<p class="MsoNormal"><br><br />
Statistics<u> U and V are point estimators of <b>a</b></u>. As the<br />
experiment runs, the empirical bias and mean square error of each<br />
estimator are recorded in the second table. The parameters a and n can<br />
be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Bias &amp; precision in parameter<br />
estimation, using Beta-distribution.</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BinomialCoinExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BinomialCoinExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of tossing n <span<br />
class="GramE">coins,</span> each with probability of heads <span<br />
class="SpellE"><b style="">p. The</b></span> <b style="">number of<br />
heads X</b> and the <b style="">proportion of heads M</b> are recorded<br />
on each <span class="SpellE">update. Either</span> <b style="">X</b><br />
or <b style="">M</b> can be selected with the list box. The discrete<br />
probability density function and moments of the selected variable are<br />
shown in blue in the distribution graph and are recorded in the<br />
distribution table. On each update, the empirical probability density<br />
function and moments of the selected variable are shown in red in the<br />
distribution graph and are recorded in the distribution table. The<br />
parameters <b style="">n</b> and <b style="">p</b> can be varied with<br />
scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Number of heads and proportion of heads in <span<br />
class="SpellE">Binomial</span> experiments</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BinomialTimelineExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BinomialTimelineExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of performing <b><i<br />
style="">n</i> Bernoulli trials</b>, each with probability of success <b<br />
style=""><i style="">p</i></b>. The successes are recorded as red dots<br />
on a timeline marked from 1 to n. The number of successes<b style=""> <i<br />
style="">X</i></b> and the proportion of successes<b style=""> <i<br />
style="">M</i></b> are recorded on each update. Either X or M can be<br />
selected with the list box. The discrete probability density function<br />
and moments of the selected variable are shown in blue in the<br />
distribution graph and are recorded in the distribution table. On each<br />
update, the empirical probability density function and moments of the<br />
selected variable are shown in red in the distribution graph and are<br />
recorded in the distribution table. The parameters n and p can be<br />
varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Number of heads and proportion of heads in <span<br />
class="SpellE">Binomial</span> experiments </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BirthdayExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BirthdayExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The birthday experiment is to <b>draw a<br />
random sample of n balls with replacement from a population of m balls,<br />
numbered from 1 to N</b>. We are interested in the random variable <b<br />
style=""><i style="">V</i></b><u> </u>that gives the number of<br />
distinct values in the sample, and the indicator variable <b style=""><i<br />
style="">I</i></b> that indicates a duplicate sample Value. On each<br />
update, the sample of balls is shown in the first graph; a ball that<br />
duplicates a previously chosen ball is shown in red, and otherwise is<br />
shown in green. The parameters m and n can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Birthday Paradox as an experiment!</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BivariateGame</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
http://www.socr.ucla.edu/htmls/SOCR_Games.html> and<br />
select “<span class="SpellE">BivariateGame</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_Games.html<span<br />
style=""></span></p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">Click in the graph to generate <span<br />
class="SpellE">bivariate</span> data. The selected points are shown as<br />
<b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
dots in the <span class="SpellE">scatter plot</span>, and the<br />
coordinates are recorded in the first table. The second table gives the<br />
<b style=""><i style="">μ</i></b> and <b style=""><i style="">σ</i></b><br />
of the x and y coordinates, and the correlation. In the graph, the<br />
horizontal cross hair is centered at the mean of the x-data and extends<br />
one standard deviation on either side. Similarly, the vertical cross<br />
hair is centered at the mean of the y-data and extends one standard<br />
deviation on either side. Finally, the least squares regression line is<br />
shown in the <span class="SpellE">scatter plot.</span></p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Regression, correlation demo</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BivariateNormalExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BivariateNormalExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment generates a point (X, Y) from<br />
a <span class="SpellE">bivariate</span> normal distribution with <b<br />
style=""><i style="">μ</i></b> (0, 0). The point is shown graphically<br />
as a <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
dot in the <span class="SpellE">scatter plot</span>, and the<br />
coordinates are recorded on each update. The distribution regression<br />
line is shown in blue in the <span class="SpellE">scatter plot</span>,<br />
and the sample regression line is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. The density function<br />
and moments of X and of Y are shown in the distribution graphs, and the<br />
moments are given in the distribution tables. The last table gives the<br />
distribution and sample correlation. The distribution standard<br />
deviations and correlations can be varied <span class="SpellE">within</span><br />
scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Regression and <span class="SpellE">correlation</span><br />
demo where the data is randomly sampled from N(<b style="">μ,σ<sup>2</sup></b>)</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BivariateUniformExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BivariateUniformExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
generates a point (X, Y) from a uniform distribution on a region of the<br />
plane. Any of the following regions can be selected with the list box: </p><br />
<p style="text-align: center;" class="MsoNormal"><span<br />
style="font-weight: bold;" class="GramE">the</span><span<br />
style="font-weight: bold;"> square</span>: -6 &lt; x &lt; 6, -6 &lt; y<br />
&lt;6; <br><br />
<span style="font-weight: bold;">the triangle</span>: -6 &lt; y<br />
&lt; x &lt; 6; and <br><br />
<span style="font-weight: bold;">the circle</span>: x<sup>2 </sup>+<br />
y<sup>2 </sup> &lt; 36.</p><br />
<p class="MsoNormal"><br><br />
The random point is shown has a <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> dot in the <span<br />
class="SpellE">scatter plot</span>, and the coordinates are recorded<br />
on each update. The <span class="SpellE">scatter plot</span> also<br />
shows the distribution regression line in blue and the sample<br />
regression line in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>.<br />
The distribution and sample density and moments for X and for Y are<br />
shown in the second and third graphs. The distribution and sample<br />
moments are given in the second and third tables. The distribution and<br />
sample correlation are given in the last table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Regression and correlation demo where the<br />
data is randomly sampled from Uniform Distribution </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BuffonCoinExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BuffonCoinExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of tossing a coin on<br />
a floor with square tiles, and is shown graphically in the first<br />
picture box. The center (X, Y) of the coin relative to the center of<br />
the square is recorded on each update in the first table, and is shown<br />
graphically as a <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
dot in the <span class="SpellE">scatter plot</span>. Variable <b<br />
style=""><i style="">I </i></b><span class="GramE">indicates</span><br />
the event that the coin crosses a crack, and is recorded on each update<br />
in the first table. The density of <b style=""><i style="">I</i></b><br />
is shown in the last graph in blue and is given in the&nbsp;second<br />
table. When the experiment runs, the empirical density of <b style=""><i<br />
style="">I</i></b> is shown in the last graph in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> and is given in the<br />
second table. The parameter of the process is the radius <b style=""><i<br />
style="">r</i></b> of the coin, and can be varied with the scroll bar</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Calculus Based Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>BuffonNeedleExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">BuffonNeedleExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal"><span class="SpellE">Buffon's</span> needle<br />
experiment consists of dropping a needle on hardwood floor, with<br />
floorboards of width 1. The experiment is shown graphically in the<br />
first graph box. The angle <b style=""><i style="">X</i></b> of the<br />
needle relative to the floorboard cracks and the distance <b style=""><i<br />
style="">Y</i></b> from the center of the needle to the lower crack<br />
are recorded in the first table on each update. Each point (X, Y) is<br />
shown as a <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
dot in the <span class="SpellE">scatter plot</span>. The variable <b<br />
style=""><i style="">I</i></b><u> </u>indicates the event that the<br />
needle crosses a crack. The density of <b style=""><i style="">I</i></b><br />
is shown in blue in the distribution graph and is recorded in the<br />
distribution table. On each update, the empirical density of <b<br />
style=""><i style="">I</i></b> is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the distribution<br />
graph and is also recorded in the distribution table. Finally, pi is<br />
shown in blue in the last graph and is recorded in the last table, and<br />
on each update, <span class="SpellE">Buffon's</span> estimate of pi is<br />
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the last graph and is recorded in the last table.<span style="">&nbsp;<br />
</span>The parameter is the needle length L, which can be varied<br />
with a scroll-bar</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Calculus Based Probability </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>CardExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">CardExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
consists of dealing n cards at random from a standard deck of 52 cards.<br />
The denomination Yi and suit <span class="SpellE">Zi</span> of the <span<br />
class="SpellE">i'th</span> card are recorded for <span class="SpellE">i</span><br />
= 1<span class="GramE">, ...,</span> n on each update. The<br />
denominations are encoded as follows: </p><br />
<p style="text-align: center;" class="MsoNormal">1<br />
(ace), 2-10, 11 (jack), 12 (queen), 13 (king).</p><br />
<p class="MsoNormal"><br><br />
The suits are encoded as follows: 0 (clubs), 1 (diamonds), 2 (hearts),<br />
3 (spades). The parameter n can be varied with a scroll bar</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ChiSquareFitExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ChiSquareFitExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
from a specified distribution and perform the <b style="">χ<sup>2</sup></b><br />
goodness of fit test to another specified distribution, at a specified<br />
level of significance. The distributions are discrete distributions on<br />
{1, 2, 3, 4, 5, 6}, and thus the experiment corresponds to rolling n<br />
dice, each governed by the same distribution.&nbsp; The sampling and<br />
test distributions can be specified by clicking on the die buttons<br />
(these bring up the die probability dialog box.&nbsp; The density of<br />
the true distribution is shown in blue in the first graph; the density<br />
of the test distribution is shown in green. The significance level can<br />
be selected from a list box and the sample size n can be varied with a<br />
scroll bar.&nbsp; The test statistic <b style=""><i style="">V</i></b><br />
has (approximately) the <b style="">χ<sup>2</sup></b><sup> </sup>distribution<br />
with 5 degrees of freedom. The density of <b style=""><i style="">V</i></b><br />
and the critical values are shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the second graph. On each<br />
update, the sample values are recorded in the first table and the<br />
sample density is shown in red in the first graph. The value of the<br />
test statistic <b style=""><i style="">V</i></b> is shown in red in<br />
the second graph. Note that the null hypothesis is rejected if and only<br />
if <b style=""><i style="">V</i></b> falls outside of the critical<br />
values. Variable <b style=""><i style="">I</i></b> <span class="GramE">indicates</span><br />
the event that the null hypothesis is rejected. The empirical density<br />
of <b style=""><i style="">I</i></b>, as the experiment runs, is shown<br />
in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the last graph and is given in the last table. The values of <b<br />
style=""><i style="">V</i></b> and <b style=""><i style="">I</i></b><br />
are recorded in the middle table on each update</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ChuckALuckExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ChuckALuckExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">In the game of chuck-a-luck, a gambler<br />
chooses an integer from 1 to 6 and then three fair dice are rolled. If<br />
exactly k dice show the gambler's number, the payoff is k<span<br />
class="GramE">:1</span>. The three dice are shown in the first picture<br />
box on each update. Random variable W gives the gambler's net profit on<br />
a $1 bet and is recorded in the first table on each update. The density<br />
and moments of W are shown in <b style=""><span style="color: blue;">blue</span></b><br />
in the second picture box and are recorded in the second table. On each<br />
update, the empirical density of <b style=""><i style="">W</i></b> is<br />
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the second picture box and recorded in the second table</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>CoinDieExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">CoinDieExperiment</span><b>:</b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The coin die experiment consists of first<br />
tossing a coin, and then rolling a red die if the coin lands head or a<br />
green die if the coin lands tails. The value of the coin (1 for heads<br />
and 0 for tails) and the score on the die that is rolled are recorded<br />
on each update. You can specify the die distribution of the dice by<br />
clicking on the die probability buttons; these buttons bring up the die<br />
probability dialog box. You can define your own distribution by typing<br />
probabilities into the text fields of the dialog box, or you can click<br />
on one of the buttons in the dialog box to specify one of the following<br />
special distributions: fair, 1-6 flat, 2-5 flat, 3-4 flat, skewed left,<br />
or skewed right. <span class="GramE">the</span> probability of heads p<br />
for the coin can be varied with a scroll bar. The density and moments<br />
of the die that is rolled are shown in the distribution graph and<br />
distribution table</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">Conditional<br />
Probability </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>CoinSampleExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">CoinSampleExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of tossing <b<br />
style=""><i style="">n</i></b> <span class="GramE">coins,</span> each<br />
with probability of heads p. Variable <span class="SpellE">Ij</span><br />
gives the outcome (1 for heads, 0 for tails) for coin <b style=""><i<br />
style="">j</i></b>. The results are recorded on each update. The<br />
parameters <b style=""><i style="">n</i></b> and <b style=""><i<br />
style="">p</i></b> can <span class="SpellE">be varied</span> with<br />
scroll bars</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability, law of large numbers</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ConfidenceIntervalExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ConfidenceIntervalExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">An experiment demonstrating the effects of <i>confidence<br />
leve</i>l and <i>sample-size</i> on the <i>size </i>of the<br />
constructed confidence interval. This experiment randomly samples from<br />
a <span class="GramE"><i>N(</i></span><b style=""><i>μ</i></b><i>=0, <b<br />
style="">σ<sup>2</sup></b>=1)</i> distribution and constructs a<br />
confidence interval for the mean (<b style=""><i>μ</i></b>). The same<br />
phenomena are observed when sampling from almost all symmetric <span<br />
class="SpellE">unimodal</span> <span class="SpellE">distributions</span>.<br />
Note how confidence interval widens as the confidence level increases.<br />
This is counterbalanced by the sample-size increase. Also, see the<br />
effect of the confidence level, <i>100(1-<b style="">α</b><span<br />
class="GramE">)%</span></i>, on the frequency of intervals missing the<br />
estimated parameter (<b style=""><i>μ</i></b><i>=0</i>, in this case).</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">Confidence intervals, margins of error.</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>CouponCollectorExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">CouponCollectorExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The coupon collector experiment consists of<br />
sampling with replacement from the population {1, 2<span class="GramE">,<br />
...,</span> m} until <b style=""><i style="">k</i></b> distinct values<br />
are obtained. The first graph gives the counts for each population<br />
value that occurred in the sample. Random variable <b style=""><i<br />
style="">W</i></b> gives the sample size and is recorded in the first<br />
table on each update. The density and moments of <b style=""><i<br />
style="">W</i></b> are shown in <b style=""><span style="color: blue;">blue</span></b><br />
in the second graph and are recorded in the second table. On each<br />
update, the empirical density and moments of W are shown in red in the<br />
second graph and are recorded in the second table. The parameters <b<br />
style=""><i style="">m</i></b> and <b style=""><i style="">k</i></b><br />
can be varied with scroll bars</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>CrapsExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">CrapsExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">In the game of craps, the shooter rolls a<br />
pair of fair die. The rules are as follows: If the shooter rolls a sum<br />
of 7 or 11 on the first roll, she wins. If the shooter rolls a sum of<br />
2, 3, or 12 on the first roll, she loses. If the shooter rolls a sum of<br />
4, 5, 6, 8, 9, or 10, this number becomes the shooter's point. The<br />
shooter continues to roll the dice until the sum is either the point<br />
(in which case she wins) or 7 (in which case she loses). Any of the<br />
following bets can be selected: Pass: this is the bet that the shooter<br />
will win, and pays 1:1. Don't Pass: this is the bet that the shooter<br />
will lose, except that an initial roll of 12 is excluded (that is, the<br />
shooter loses, but <span class="GramE">the don't</span> pass bettor<br />
neither wins nor loses). The bet pays 1:1. Field: this is a bet on a<br />
single throw. <br><br />
<br><br />
It pays 1:1 if 3, 4, 9, 10, or 11 is thrown, 2:1 if 2 or 12 is thrown,<br />
and loses otherwise. Craps: this is a bet that 2, 3, or 12 will come up<br />
on a single throw, and pays 7:1. Craps 2: this is a bet that 2 will<br />
come up on a single throw, and pays 30:1. Craps 3: this is a bet that 3<br />
will come up on a single throw, and pays 15:1. Craps 12: this is a bet<br />
that 12 will come up on a single throw, and pays 30:1. Seven: this is a<br />
bet that 7 will come up on a single throw, and pays 4:1. Eleven: this<br />
is a bet that 11 will come up on a single throw, and pays 15:1. Big 6.<br />
This is a bet that 6 will be thrown before 7, and pays 1:1. Big 8: this<br />
is a bet that 8 will be thrown before 7, and pays 1:1. <span<br />
class="SpellE">Hardway</span> 4: this is a bet that (2, 2) will be<br />
thrown before 7 or any other 4, and pays 7:1. <span class="SpellE">Hardway</span><br />
6. <span class="GramE">this</span> is a bet that (3, 3) will be thrown<br />
before 7 or any other 6, and pays 9:1. <span class="SpellE">Hardway</span><br />
8: this is a bet that (4, 4) will be thrown before 7 or any other 8,<br />
and pays 9:1. <span class="SpellE">Hardway</span> 10: this is a bet<br />
that (5, 5) will be thrown before 7 or any other 10, and pays 7:1</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>DiceExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">DiceExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of rolling <b<br />
style=""><i style="">n</i></b> dice, each governed by the same<br />
probability distribution. You can specify the die distribution by<br />
clicking on the die probability button; <span class="GramE">this<br />
button bring</span> up the die probability dialog box. You can define<br />
your own distribution by typing probabilities into the text fields of<br />
the dialog box, or you can click on one of the buttons in the dialog<br />
box to specify one of the following special distributions<span<br />
class="GramE">:</span><br><br />
<br><br />
</p><br />
fair, 1-6 flat, 2-5 flat, 3-4<br />
flat, skewed left, or skewed right. <br><br />
<p class="MsoNormal"> <br><br />
The following random variables are recorded on each update: the sum of<br />
the scores <b style=""><i style="">Y</i></b>, the <span class="GramE">average<br />
score</span> <b style=""><i style="">M</i></b>, the minimum score <b<br />
style=""><i style="">U</i></b> the maximum score <b style=""><i<br />
style="">V</i></b>, the number of aces (1's) <b style=""><i style="">Z</i></b>.<br />
Any one of these variables can be selected with a list box. The density<br />
and moments of the selected variable are shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the distribution graph and are<br />
recorded in the distribution table. When the simulation runs, the<br />
empirical density and moments are shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the distribution<br />
graph and are recorded in the distribution table. The parameter <b<br />
style=""><i style="">n</i></b> can be varied with a scroll bar.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Discrete variables</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>DiceSampleExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">DiceSampleExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of rolling <b<br />
style=""><i style="">n</i></b> dice, each governed by the same<br />
probability distribution. You can specify the die distribution by<br />
clicking on the die probability button; this button brings up the die<br />
probability dialog box. You can define your own distribution by typing<br />
probabilities into the text fields of the dialog box, or you can click<br />
on one of the buttons in the dialog box to specify one of the following<br />
special distributions: fair, 1-6 flat, 2-5 flat, 3-4 flat, skewed left,<br />
or skewed right. The number of dice can be varied with a scroll bar.<br />
The scores of each die are recorded in the table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>DieCoinExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">DieCoinExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The die coin experiment consists of rolling<br />
a die and then tossing a coin the number of times shown on the die. The<br />
die score <b style=""><i style="">X</i></b> and the number of heads <b<br />
style=""><i style="">Y</i></b> are recorded on each update. The<br />
density function and moments of <b style=""><i style="">Y</i></b> are<br />
shown in <b style=""><span style="color: blue;">blue</span></b> in the<br />
second graph and are recorded in the second table. On each update, the<br />
empirical density and moments of <b style=""><i style="">Y</i></b> are<br />
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the second graph and are recorded in the second table.&nbsp; The<br />
probability of heads for the coin can be varied with the scroll bar.<br />
You can specify the die distribution by clicking on the die probability<br />
button; this button brings up the die probability dialog box.<br><br />
</p><br />
<p class="MsoNormal"><br><br />
You can define your own distribution by typing probabilities into the<br />
text fields of the dialog box, or you can click on one of the buttons<br />
in the dialog box to specify one of the following special<br />
distributions: fair, 1-6 flat, 2-5 flat, 3-4 flat, skewed left, or<br />
skewed right.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">Inversion of<br />
conditioning in conditional probability calculations:</p><br />
<p class="MsoNormal">P(D3<br />
| 2H) = <br><br />
P(2H | D3) P(D3) / P(2H)</p><br />
<p class="MsoNormal"><br><br />
RHS = difficult;&nbsp;&nbsp;&nbsp; LHS can be computed exactly (not<br />
hard). Validate empirically that the two are approximately equal. Demo<br />
SOCR Dice-Coin Experiment<br><br />
http://www.socr.ucla.edu/">http://www.socr.ucla.edu/</a><span<br />
style="font-size: 10pt;"> </span></p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ErrorGame</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
http://www.socr.ucla.edu/htmls/SOCR_Games.html> and<br />
select “<span class="SpellE">ErrorGame</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_Games.html</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">Click on the horizontal axis in the first<br />
graph to select points for a frequency distribution. The frequency<br />
distribution is given in the first table, and the corresponding<br />
histogram is shown in the first graph. The class width (and hence the<br />
number of classes) can be varied with the scroll bar. The vertical axis<br />
can be selected as either frequency or relative frequency from the list<br />
box.&nbsp; The second graph shows the error function, which can be<br />
selected as either mean square error or mean absolute error. In the<br />
first case, the minimum occurs at the mean <b style=""><i style="">μ</i></b><br />
and the minimum value is the variance <b style=""><i style="">σ<sup>2</sup></i></b>.<span<br />
style="">&nbsp; </span>In the second case, the minimum occurs<br />
throughout the median interval and the minimum value is the mean<br />
absolute deviation from the median.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>Exponential<br />
Experiment:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “Exponential Experiment” from the list.<span style="">&nbsp;<br />
</span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This experiment takes random<br />
samples from a user defined exponential distribution and plots the<br />
observed results (in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>)<br />
against the theoretical distribution (in <b style=""><span<br />
style="color: blue;">blue</span></b>).&nbsp; The observed value for<br />
each trial is displayed beneath the distribution in the left column.<br />
The theoretical and observed <b style=""><i style="">μ</i></b> and <b<br />
style=""><i style="">σ</i></b> are displayed beneath the distribution<br />
in the right column.&nbsp; </p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">Exponential Distribution</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>FiniteOrderStatisticExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">FiniteOrderStatisticExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of selecting <b<br />
style=""><i style="">n</i></b> balls at random (without replacement)<br />
from a population of <b style=""><i style="">N</i></b> balls, numbered<br />
from 1 to N. For <span class="SpellE"><b style=""><i style="">i</i></b></span><b<br />
style=""><i style=""> </i></b>= 1, 2<span class="GramE">, ...,</span><br />
n, the <span class="SpellE">i'th</span> smallest number in the sample,<br />
<b style=""><i style="">X(<span class="SpellE">i</span>)</i></b><br />
(the <span class="SpellE">i'th</span> order statistic), is recorded on<br />
each update. For a selected <b style=""><i style="">k</i></b>, the<br />
distribution and moments of <span class="GramE"><b style=""><i style="">X(</i></b></span><b<br />
style=""><i style="">k)</i></b> are shown in the distribution graph<br />
and the distribution table. The parameters <b style=""><i style="">N,<br />
n, and k</i></b> can be varied with scroll bars</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>FireExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">FireExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The forest consists of a rectangular lattice<br />
of trees. Each tree in the forest<br><br />
is in one of three possible states: Healthy trees are colored <b<br />
style=""><span style="color: green;">green</span></b>; on fire trees<br />
are colored <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>;<br />
burnt trees are colored <b style="">black</b>. A tree that is on fire<br />
at time <b style=""><i style="">t</i></b> will be burnt at time t + 1;<br />
once a tree is burnt it remains burnt; if a tree is healthy at time t<br />
and is directly above or below or to the right or to the left of a tree<br />
on fire at time t, then the healthy tree will catch on fire at time, t<br />
+ 1 independently, with respective probabilities <span class="SpellE"><b<br />
style=""><i style="">pu</i></b></span><b style=""><i style="">,<span<br />
class="GramE">&nbsp; pd</span>, pr, and pl</i></b>. The forest is<br />
shown in the large graph box in the center. You can choose either a100<br />
by 50 <span class="GramE">forest</span> or a 500 by 250 forest. To<br />
change the state of a tree, select the desired state with the list box<br />
and then click on the tree. The fire spread probabilities can be varied<br />
with scroll bars. The number of trees that are healthy, on fire, and<br />
burnt are recorded at each time unit in the table</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>GaltonBoardExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">GaltonBoardExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The <span class="SpellE">Galton</span><br />
board experiment consists of performing <b style=""><i style="">n</i></b><br />
Bernoulli trials with probability of success <b style=""><i style="">p</i></b>.<br />
The trial <span class="GramE">outcome are</span> represented<br />
graphically as a path in the <span class="SpellE">Galton</span> board:<br />
success corresponds to a bounce to the right and failure to a bounce to<br />
the left. The number of successes <b style=""><i style="">X</i></b><br />
and the proportion of successes <b style=""><i style="">M</i></b> are<br />
recorded on each update. Graphically, <b style=""><i style="">X</i></b><br />
is the number of the peg in the last row of the <span class="SpellE">Galton</span><br />
board that the ball hits. The distribution and moments of the selected<br />
variable (X or M) are given in the distribution graph and the<br />
distribution table. The parameters <b style=""><i style="">n</i></b><br />
and <b style=""><i style="">p</i></b> can be varied with scroll bars</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal"><span style="">Quincunx, <span<br />
class="SpellE">Galton</span> Board Game</span></p><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>GaltonBoardGame</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
http://www.socr.ucla.edu/htmls/SOCR_Games.html> and<br />
select “<span class="SpellE">GaltonBoardGame</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_Games.html</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">Click the left arrow button to move the ball<br />
to the left and the right arrow button to move the ball to the right.<br />
The bit string is recorded in the table below, as well as the<br />
corresponding subset. Finally, the last table entry gives the current<br />
ball location and the corresponding binomial coefficient</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal"><span style="">Quincunx, <span<br />
class="SpellE">Galton</span> Board Game</span></p><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>GammaEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">GammaEstimateExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
is to generate a random sample X1, X2<span class="GramE">, ...,</span> <span<br />
class="SpellE">Xn</span> of size <b style=""><i style="">n</i></b><br />
from the <b style=""><i style="">Γ </i></b>distribution with shape<br />
parameter <b style=""><i style="">k</i></b> and scale parameter <b<br />
style=""><i style="">b</i></b>. The distribution density is shown in <b<br />
style=""><span style="color: blue;">blue</span></b> in the graph, and<br />
on each update, the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. On each update, the<br />
following statistics are recorded: </p><br />
<p style="text-align: center;" class="MsoNormal">U<br />
= M<sup>2 </sup> / T<sup>2 </sup>, V = T<sup>2 </sup> / M, W = M / k<br><br />
where M = (X<sub>1</sub> + X<sub>2</sub> + ••• + <span class="SpellE">X</span><sub>n</sub>)<br />
/ n and <br><br />
T<sup>2 </sup> = [(X<sub>1</sub><span style="font-weight: bold;"></span><br />
- M)<sup>2 </sup> + (X<sub>2</sub> - M)<sup>2 </sup> + ••• + (<span<br />
class="SpellE">X</span><sub>n</sub> - M)<sup>2</sup>] / n</p><br />
<p class="MsoNormal"><br><br />
Statistic <b style=""><i style="">U</i></b> is a point estimator of <b<br />
style=""><i style="">k</i></b> and statistics <b style=""><i style="">V</i></b><br />
and <b style=""><i style="">W</i></b> are point estimators of <b<br />
style=""><i style="">b</i></b>. As the experiment runs, the empirical<br />
bias and mean square error of each estimator are recorded in the second<br />
table. The parameters <b style=""><i style="">k, b, and n</i></b> can<br />
be varied with scroll bars</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>GammaExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">GammaExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The <b style=""><i style="">Γ</i></b><br />
experiment consists of running a Poisson process until the time of the <span<br />
class="SpellE">k'th</span> arrival. The arrivals are shown as <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b> dots in<br />
the timeline. The density function of the <span class="SpellE">k'th</span><br />
arrival <span class="SpellE"><b style=""><i style="">Tk</i></b></span><br />
is shown in the graph box, and the moments are given in the<br />
distribution table. The arrival times are recorded in the update table.<br />
The parameters are the rate of the process <b style=""><i style="">r </i></b>and<br />
the arrival number <b style=""><i style="">k</i></b>, which can be<br />
varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>General<br />
Birthday Experiment</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “General Birthday Experiment<b></b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This experiment illustrates the<br />
birthday paradox.&nbsp; The experiment makes a histogram plot of the<br />
expected proportions (<b style=""><span style="color: blue;">blue</span></b>)<br />
and the observed proportions (<b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>) of the number of<br />
people who do not share the same birthday.&nbsp; The theoretical and<br />
observed <b style=""><i style="">μ, σ, and proportions</i></b> of<br />
people who do not share the same birthday are displayed underneath the<br />
histograms in the right column.&nbsp; The results of each experiment<br />
are the left column.&nbsp; </p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">Birthday Paradox as an experiment</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>MarkovChainExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">MarkovChainExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This applet illustrates a basic Markov chain<br />
on the <span class="GramE">states {0</span>, 1, ..., <b style=""><i<br />
style="">n</i></b>}. The states are represented as balls, and the<br />
current state is colored red. The number of states can be varied, as<br />
well as the transition probabilities. The initial state can be<br />
specified by clicking on a ball when the time is 0. The graph and table<br />
show the proportion of time spent in each state.&nbsp; As the time<br />
increases, these proportions converge to the steady-state<br />
distribution&nbsp; of the chain.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>MatchExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">MatchExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The matching experiment is to randomly<br />
permute <b style=""><i style="">n</i></b> balls, numbered 1 to n. A<br />
match occurs whenever the ball number and the position number agree.<br />
The matches are shown in red. The number of matches <b style=""><i<br />
style="">N</i></b> is recorded on each update. The distribution and<br />
moments of N are shown in the distribution graph and the distribution<br />
table. The parameter n can be varied with a scroll bar.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Permutations&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>MeanEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">MeanEstimateExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This class models the interval estimation<br />
experiment in the standard <span class="GramE">N(</span><span<br />
style="font-style: italic;">μ, σ</span><sup>2</sup>) model. A random<br />
sample from <span class="GramE">N(</span><span<br />
style="font-style: italic;">μ, σ</span><sup style="font-style: italic;">2</sup>)<br />
is simulated, and then an interval estimate of μ is computed. The user<br />
can choose whether to compute the interval based on the standard normal<br />
statistic or the student t statistic. The confidence level and sample<br />
size can be chosen.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>MeanTestExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">MeanTestExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size <b style=""><i style="">n</i></b> from a selected distribution<br />
and then test a hypothesis about the mean <b style=""><i style="">µ</i></b><br />
at a specified significance level. The distribution can be selected<br />
from a list box; the options are the <span class="GramE"><b style=""><i<br />
style="">N(</i></b></span><b style=""><i style="">μ, σ<sup>2</sup>)</i></b>,<br />
<b style=""><i style="">Γ</i></b>, and uniform distributions. In<br />
each case, the appropriate parameters and the sample size n can be<br />
varied with scroll bars. The significance level can be selected with a<br />
list box, as can the type of test: two-sided, left-sided, or<br />
right-sided. The boundary point <b style=""><i style="">m<sub>o</sub></i></b><br />
between the null and alternative hypotheses can be varied with a scroll<br />
bar. The density of the distribution and µ are shown in blue in the<br />
first graph; <b style=""><i style="">m</i></b><b style=""><i style=""><sub>o</sub></i></b><br />
is shown in green. The<br />
test can be constructed under the assumption that the <b style=""><i<br />
style="">σ</i></b> of the distribution is known or unknown. In the<br />
first case, the test statistic has the standard <span class="GramE"><b<br />
style=""><i style="">N(</i></b></span><b style=""><i style="">μ,σ<sup>2</sup>)</i></b><br />
distribution; in the second case the test statistics has the student t<br />
distribution with n - 1 degrees of freedom. The density and the<br />
critical values of the test statistic are shown in the second graph in <b<br />
style=""><span style="color: blue;">blue</span></b>. On each update,<br />
the sample<br />
density is shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the first graph and the sample values are recorded in the first<br />
table. The sample mean <b style=""><i style="">M</i></b> is shown in <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b> in the<br />
first graph and the value of the test statistics (<b style=""><i<br />
style="">Z or T</i></b>) is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the second graph.<br />
The variable <b style=""><i style="">I</i></b> <span class="GramE">indicates</span><br />
the event that the null hypothesis is rejected. On each update, <b<br />
style=""><i style="">M, Z or T, and I</i></b><br />
are recorded in the second table. Note that the null hypothesis is<br />
reject (I = 1) if and only if the test statistic (Z or T) falls outside<br />
of the critical values. Finally, the empirical density of <b style=""><i<br />
style="">I </i></b>is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the last graph and<br />
recorded in the last table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Hypothesis Testing</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>Mixture<br />
EM Experiment</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “Mixture EM Experiment<b></b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This experiment uses the expectation<br />
maximization algorithm to calculate the parameters for the mixture<br />
distribution.&nbsp; The user decides whether or not to use the gauss<br />
mix or a linear mix.&nbsp; After deciding the number of mixtures,<br />
clicking the <span style="font-style: italic; font-weight: bold;">EM<br />
run</span> will generate the distributions according to the<br />
algorithm.&nbsp; To observe a different result, clicking the <span<br />
style="font-weight: bold; font-style: italic;">Init<br />
Kernels</span> button will generate new mixtures.&nbsp; Each color on<br />
the<br />
graph represents a different mixture.&nbsp; The weight of each mixture<br />
is depicted on the graph in the same color as the distribution.&nbsp;<br />
The mean log likelihood is always displayed in red.&nbsp; </p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">Mixture Distribution, Expectation<br />
maximization algorithm.&nbsp; </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>MontyHallExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">MontyHallExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">In the Monty Hall experiment, there are<br />
three doors; a car is behind one and goats are behind the other two.<br />
The player selects a door and then the host opens one of the other two<br />
doors. The player can then stay with her original selection or switch<br />
to the remaining unopened door. The door finally selected by the player<br />
is opened and she either wins or loses. Either of two host strategies<br />
can be selected with the list box. In the standard strategy, the host<br />
always opens a door with a goat); in the blind strategy, the host<br />
randomly opens one of the two doors available to him. The player<br />
switches doors with probability <span class="GramE"><b style=""><i<br />
style="">p</i></b>, that</span> can be varied with a scroll bar.<br />
Variable <b style=""><i style="">G</i></b> indicates the event that<br />
the host opened a door with a goat; variable <b style=""><i style="">S</i></b><br />
indicates the event that the player switched doors; and variable <b<br />
style=""><i style="">W</i></b> indicates the event that the player won<br />
the car. The density of <b style=""><i style="">W</i></b> is shown in<br />
the distribution graph and the distribution table</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;Probabilities<span class="GramE">:</span><br><br />
W = {Win}; <br><br />
O={first chosen card is the diamond}<br><br />
<br><br />
1. Never-Swap (stay home) Strategy:<br><br />
P(W)=P(W|O)P(O)+P(<span class="SpellE">W|O<sup>c</sup></span>)P(<span<br />
class="SpellE">O<sup>c</sup></span>)<br><br />
P(W)= 1 * 1/3 + 0 * 2/3 = 1/3<br><br />
<br><br />
2. Always-Swapping Strategy:<br><br />
P(W)=P(W|O)P(O)+P(<span class="SpellE">W|O<sup>c</sup></span>)P(<span<br />
class="SpellE">O<sup>c</sup></span>)<br><br />
P(W)= 0 * 1/3 + 1 * 2/3 = 2/3</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>MontyHallGame</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
http://www.socr.ucla.edu/htmls/SOCR_Games.html> and<br />
select “<span class="SpellE">MontyHallGame</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_Games.html</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">In the Monty Hall game, there are three<br />
doors; a car is behind one and goats are behind the other two. Click on<br />
the Play button to start a new game. Then select a door by clicking.<br />
The host will open one of the other two doors. Finally select a door<br />
again (you may stick with your original selection or switch). This door<br />
is opened and you either win or lose.<br><br />
Either of two host strategies can be selected with the list box. In the<br />
standard strategy, the host always opens a door with a goat); in the<br />
blind strategy, the host randomly opens one of the two doors available<br />
to him. Variable <b style=""><i style="">G </i></b>indicates the<br />
event that the host opened a door with a goat; variable <b style="">S</b><br />
indicates the event that you switched doors from your first<br><br />
selection to your second; and variable <b style=""><i style="">W</i></b><br />
indicates the event that you win the car. The empirical distribution of<br />
<b style=""><i style="">W</i></b> is shown in the distribution<br />
graph and is recorded in the distribution table</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Conditional Probabilities<span class="GramE">:</span><br><br />
W = {Win}; <br><br />
O={first chosen card is the diamond}<br><br />
<br><br />
1. Never Swap Strategy:<br><br />
P(W)=P(W|O)P(O)+P(<span class="SpellE">W|O<sup>c</sup></span>)P(<span<br />
class="SpellE">O<sup>c</sup></span>)<br><br />
P(W)= 1 * 1/3 + 0 * 2/3 = 1/3<br><br />
<br><br />
2. Always Swapping Strategy:<br><br />
P(W)=P(W|O)P(O)+P(<span class="SpellE">W|O<sup>c</sup></span>)P(<span<br />
class="SpellE">O<sup>c</sup></span>)<br><br />
P(W)= 0 * 1/3 + 1 * 2/3 = 2/3 </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>NegativeBinomialExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">NegativeBinomialExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The negative binomial experiment consists of<br />
performing Bernoulli trials, with probability of success <b style=""><i<br />
style="">p</i></b>, until the <span class="SpellE"><b style=""><i<br />
style="">k</i></b>'th</span> success occurs. The successes are shown<br />
as red dots in the timeline. The number of trials <b style=""><i<br />
style="">Y</i></b> is recorded on each update. The density and moments<br />
of <b style=""><i style="">Y</i></b> are shown in the distribution<br />
graph and the distribution table. The parameters <b style=""><i<br />
style="">k</i></b> and <b style=""><i style="">p</i></b><br><br />
can be varied with scroll bars</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Binomial distribution</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>NormalEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">NormalEstimateExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
is to generate a random sample X<span class="SpellE"><sub>1</sub></span>,<br />
X<span class="SpellE"><sub>2</sub></span><span class="GramE">, ...,</span><br />
<span class="SpellE">X</span><span class="SpellE"><sub>n</sub></span><br />
of size n from the <b style=""><i style="">N(μ,σ<sup>2</sup>)</i></b><br />
distribution with mean μ and standard deviation <b style=""><i style="">σ</i></b>.<br />
The distribution density is shown in blue in the graph, and on each<br />
update, the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. On each update, the<br />
following statistics are recorded:</p><br />
<p style="text-align: center;" class="MsoNormal">M<br />
= (X<span class="SpellE"><sub>1</sub></span> + X<span class="SpellE"><sub>2</sub></span><br />
+ ••• + <span class="SpellE">X</span><span class="SpellE"><sub>n</sub></span>)<br />
/ n,<br><br />
S<sup>2 </sup> = [(X<span class="SpellE"><sub>1</sub></span> - M)<sup>2<br />
</sup> + (X<span class="SpellE"><sub>2</sub></span> - M)<sup>2 </sup><br />
+ ••• + (<span class="SpellE">X</span><span class="SpellE"><sub>n</sub></span><br />
- M)<sup>2 </sup>] / (n - 1)<br><br />
T<sup>2 </sup> = [(X<span class="SpellE"><sub>1</sub></span> - M)<sup>2<br />
</sup> + (X<span class="SpellE"><sub>2</sub></span> - M)<sup>2 </sup><br />
+ ••• + (<span class="SpellE">X</span><span class="SpellE"><sub>n</sub></span><br />
- M)<sup>2 </sup>] / n<br><br />
W<sup>2 </sup> = [(X<span class="SpellE"><sub>1</sub></span> - m)<sup>2<br />
</sup> + (X<span class="SpellE"><sub>2</sub></span> - m)<sup>2 </sup><br />
+ ••• + (<span class="SpellE">X<sub>n</sub></span> - m)<sup>2 </sup>]<br />
/ n.</p><br />
<p class="MsoNormal"><br><br />
The statistic <b style=""><i style="">M</i></b> is a point estimator<br />
of the distribution mean <b style=""><i style="">μ</i></b> and the<br />
statistics <b style=""><i style="">S<sup>2</sup>, T<sup>2</sup>, and W<sup>2</sup></i></b><br />
are point estimators of the distribution variance <b style=""><i<br />
style="">σ<sup>2</sup></i></b>. As the experiment runs, the empirical<br />
bias and mean square error of each estimator are recorded in the second<br />
table. The parameters <b style=""><i style="">m, d, and n</i></b> can<br />
be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>OrderStatisticExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">OrderStatisticExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of selecting a<br />
random sample of size <b style=""><i style="">n</i></b> from a<br />
specified distribution. The sampling distribution can be selected as<br />
either the uniform distribution on (0, 1) or the exponential<br />
distribution with parameter 1. The first graph shows the density<br />
function and moments of the sampling distribution in blue. For each run<br />
of the experiment, the sample density and moments are shown in <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b>. The<br />
sample values are arranged in increasing order (these are the order<br />
statistics) and recorded in first table. For a specified <b style=""><i<br />
style="">k</i></b>, the <span class="SpellE">k'th</span> order<br />
statistic is recorded on each update in the second table. The density<br />
and moments of <span class="GramE"><b style=""><i style="">X(</i></b></span><b<br />
style=""><i style="">k)</i></b> are shown in the second graph in <b<br />
style=""><span style="color: blue;">blue</span></b>. As the experiment<br />
runs, the empirical density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. The moments of <span<br />
class="GramE">X(</span>k) are given in the last table. As the<br />
experiment runs, the empirical moments are given also. The parameters <b<br />
style=""><i style="">n and k</i></b> can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ParetoEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ParetoEstimateExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
is to generate a random sample X1, X2, ..., <span class="SpellE">Xn</span><br />
of size <b style=""><i style="">n</i></b> from the Pareto distribution<br />
with parameter <b style=""><i style="">a</i></b>. The distribution<br />
density is shown in blue in the graph, and on each update, the sample<br />
density is shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>.<br />
On each update, the following statistics are recorded: </p><br />
<p style="text-align: center;" class="MsoNormal">U<br />
= M / (M - 1) where M = (X<span class="SpellE"><sub>1</sub></span> + X<span<br />
class="SpellE"><sub>2</sub></span> + ••• + <span class="SpellE">X</span><span<br />
class="SpellE"><sub>n</sub></span>) / n<br><br />
V = n / [<span class="SpellE">ln</span>(X<span class="SpellE"><sub>1</sub></span>)<br />
+ <span class="SpellE">ln</span>(X<span class="SpellE"><sub>2</sub></span>)<br />
+ ••• + <span class="SpellE"><span class="GramE">ln</span></span><span<br />
class="GramE">(</span><span class="SpellE">X</span><span class="SpellE"><sub>n</sub></span>)].<br />
</p><br />
<p class="MsoNormal"><br><br />
Statistics <b style=""><i style="">U</i></b> and <b style=""><i<br />
style="">V</i></b> are point estimators of <b style=""><i style="">a</i></b>.<br />
As the experiment runs, the empirical bias and mean square error of<br />
each estimator are recorded in the second table. The parameters a and n<br />
can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>PointExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">PointExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of tossing coins,<br />
each with probability of heads <b style=""><i style="">p</i></b>,<br />
until either <b style=""><i style="">n</i></b> heads occur or <b<br />
style=""><i style="">m</i></b> tails occur. The event that <b style=""><i<br />
style="">n</i></b> heads occur before <b style=""><i style="">m</i></b><br />
tails is indicated by the random variable <b style=""><i style="">I</i></b>.<br />
On each update, the results of the coin tosses are shown in the first<br />
graph. On each update, the number of heads, the number of tails, and<br />
the value of <b style=""><i style="">I</i></b><span<br />
style="font-style: italic;"><span style="font-weight: bold;"> </span></span>are<br />
recorded in the first table. The density of <b style=""><i style="">I</i></b><br />
is shown in blue in the second graph and is recorded in the second<br />
table. On each update, the empirical density of <b style=""><i style="">I<br />
</i></b>is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the second graph<br />
and is recorded in the second table. The parameters <b style=""><i<br />
style="">n, m, and p</i></b> can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>Poisson2DExperiment:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “Poisson2DExperiment” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to run a Poisson process<br />
in the plane, and record the number of points <b style=""><i style="">N</i></b><br />
in the square [0, w] x [0, w]. The points are shown as <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> dots in the <span<br />
class="SpellE">scatter plot</span>. The number of points <b style=""><i<br />
style="">N</i></b> is recorded on each update. The density and moments<br />
of <b style=""><i style="">N</i></b> are shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the distribution graph and are<br />
recorded in the distribution table. On each update, the empirical<br />
density of <b style=""><i style="">N</i></b> is shown in red in the<br />
distribution graph and is recorded in the distribution table. The<br />
parameters of the experiment are the rate <b style=""><i style="">r</i></b><br />
of the process and the side length <b style=""><i style="">w</i></b><br />
of the square, which can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">2D Poisson Distribution</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>PoissonExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">PoissonExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment to run a Poisson process<br />
until time <b style=""><i style="">t</i></b>. The arrivals are shown<br />
as red dots on a timeline, and the number of arrivals N is recorded on<br />
each update. The density and moments of <b style=""><i style="">N</i></b><br />
are shown in the distribution graph and the distribution table. The<br />
parameters of the experiment are the rate of the process <b style=""><i<br />
style="">r</i></b> and the time <b style=""><i style="">t,</i></b><br />
which can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">1D Poisson Distribution</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>PoissonSplitExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">PoissonSplitExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to run a Poisson process<br />
until time <b style=""><i style="">t</i></b>. Each arrival is type 1<br />
with probability <b style=""><i style="">p</i></b> or type 0 with<br />
probability 1 - p. In the timeline, the type 1 arrivals are shown as <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b> dots<br />
and the type 0 arrivals as green dots. The number of type 1 arrivals M<br />
and the number of type 0 arrivals N are recorded on each update. The<br />
densities and moments of M and N are shown in the distribution graphs<br />
and the distribution tables. The parameters are the rate of the process<br />
r, the time t, and the probability p. These can be varied with scroll<br />
bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>PokerDiceExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">PokerDiceExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The poker dice experiment consists of<br />
rolling 5 fair dice. Random variable <b style=""><i style="">V</i></b><br />
denotes the value of the hand; V = 0: all distinct, V = 1: one pair, V<br />
= 2: two pair, V = 3: three of a kind, V = 4: full house, V = 5: four<br />
of a kind, V = 6: five of a kind. The die scores<span class="GramE">&nbsp;<br />
and</span> the value V are recorded on each update in the first table.<br />
The density function of V is shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the<br />
graph and recorded in the second table. On each update, the empirical<br />
density function of V is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the graph and<br />
recorded in the second table. In the stop frequency list box, you can<br />
set the simulation to stop automatically when <b style=""><i style="">V</i></b><br />
is a particular value.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>PokerExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">PokerExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The poker experiment consists of dealing 5<br />
cards at random from a standard deck of 52 cards. <b style=""><i<br />
style="">V</i></b> denotes the value of the hand; V = 0: no value, V =<br />
1: one pair, V = 2: two pair V = 3: three of a kind, V = 4: straight, V<br />
= 5: flush, V = 6: full house, V = 7: four of a kind, V = 8: straight<br />
flush. The value V is recorded on each update in the first table. The<br />
density function of <b style=""><i style="">V</i></b> is shown in <b<br />
style=""><span style="color: blue;">blue</span></b> in the graph and<br />
recorded in the second table. On each update, the empirical density<br />
function of <b style=""><i style="">V</i></b> is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the graph and<br />
recorded in the second table. In the stop frequency list box, you can<br />
set the simulation to stop automatically when <b style=""><i style="">V</i></b><br />
is a particular value.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ProbabilityPlotExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ProbabilityPlotExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size <b style=""><i style="">n</i></b> from a specified<br />
distribution and graphically test the data against a hypothesized<br />
parametric family of distributions. The sampling distribution can be<br />
chosen from the list box; the options are the <span class="GramE"><b<br />
style=""><i style="">N(</i></b></span><b style=""><i style="">μ,σ<sup>2</sup>)</i></b>,<br />
exponential, and uniform; in each case the appropriate parameters can<br />
be varied with scroll bars. Similarly, the test distribution can be<br />
selected from a list box; the options are the standard <span<br />
class="GramE"><b style=""><i style="">N(</i></b></span><b style=""><i<br />
style="">μ,σ<sup>2</sup>)</i></b>, the uniform distribution on (0, 1),<br />
or the exponential distribution with parameter 1. The density function<br />
of the sampling distribution is shown in the first graph in <b style=""><span<br />
style="color: blue;">blue</span></b>, and on each update, the sample<br />
values are shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>.<br />
The sample values are arranged in increasing order (these are the order<br />
statistics) and recorded in the first table on each update. The density<br />
function of the test distribution is shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in<br />
the second graph. The <span class="SpellE">quantiles</span> of order <span<br />
class="SpellE">i</span> / (n + 1) for <span class="SpellE">i</span> =<br />
1, 2<span class="GramE">, ...,</span> n are shown in red in the second<br />
graph and are recorded in the second table. On each update, the order<br />
statistic-<span class="SpellE">quantile</span> pairs are plotted in the<br />
third graph (this is the probability plot).</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>Problem<br />
of Points Experiment</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “Problem of Points Experiment<b></b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This game illustrates the famous<br />
problem of points devised during the renaissance period.&nbsp; The<br />
player <b style=""><i style="">n</i></b> wins when a user specified<br />
number of heads appears.&nbsp; The player <b style=""><i style="">m</i></b><br />
wins when a user specified number of tails wins.&nbsp; The game<br />
continues until one player wins.&nbsp; The theoretical probability of<br />
each player winning is illustrated in the <b style=""><span<br />
style="color: blue;">blue</span></b> histogram, while the observed<br />
proportion of wins is depicted with the <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> histogram.&nbsp; The<br />
results of each trial are displayed in the left half of the green<br />
section.&nbsp; In this half, the first column is the experiment number,<br />
the second column is the number of heads rolled, the third column is<br />
the number of tails rolled, and the fourth column depicts the<br />
winner.&nbsp; The number “1” indicates that player “n” won, while the<br />
number “0” indicates that player “m” won. The<br />
theoretical and observed μ, σ, and proportions are displayed in the<br />
right green half.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">The famous problem of points as an<br />
experiment.&nbsp; </p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ProportionEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ProportionEstimateExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size <b style=""><i style="">n</i></b> from the Bernoulli<br />
distribution with parameter p, and then to construct an approximate<br />
confidence interval for p at a specified confidence level. The true<br />
value of <b style=""><i style="">p</i></b> can be varied with a scroll<br />
bar. The density of the Bernoulli distribution and the <span<br />
class="SpellE">the</span> value of p are shown in blue in the first<br />
graph. The confidence level can be selected from a list box, as can the<br />
type of interval--two sided, upper bound, or lower bound. The interval<br />
is constructed using <span class="SpellE">quantiles</span> from the<br />
standard <span class="GramE"><b style=""><i style="">N(</i></b></span><b<br />
style=""><i style="">μ,σ<sup>2</sup>)</i></b>. The standard normal<br />
density and the critical values are shown in blue in the second graph.<br />
Variables <b style=""><i style="">L</i></b> and <b style=""><i<br />
style="">R</i></b> denote the left and right endpoints of the<br />
confidence interval and <b style=""><i style="">I</i></b> indicates<br />
the event that the confidence interval contains <b style=""><i style="">p</i></b>.<br />
The theoretical density of <b style=""><i style="">I</i></b> is shown<br />
in <b style=""><span style="color: blue;">blue</span></b> in the third<br />
graph. On each update, the sample density and the confidence interval<br />
are shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the first graph, and the computed standard score is shown in <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b> in the<br />
second graph. Note that the confidence interval contains p in the first<br />
graph if and only if the standard score falls between the critical<br />
values in the second graph. The third graph shows the proportion of<br />
successes and failures in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. The first table gives<br />
the sample values; the second table records <b style=""><i style="">L,<br />
R,</i></b> the standard score <b style=""><i style="">Z, and I</i></b>.<br />
Finally, the third table gives the theoretical and empirical densities<br />
of <b style=""><i style="">I.</i></b></p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>ProportionTestExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">ProportionTestExperiment</span><b>:</b>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size <b style=""><i style="">n</i></b> from the Bernoulli<br />
distribution with parameter <b style=""><i style="">p</i></b>, and<br />
then test a hypothesis about <b style=""><i style="">p</i></b> at a<br />
specified significance level. The sample size <b style=""><i style="">n</i></b><br />
can be varied with a scroll bar. The significance level can be selected<br />
with a list box, as can the type of test: two-sided, left-sided, or<br />
right-sided. The boundary point <b style=""><i style="">p0</i></b><br />
between the null and alternative hypotheses can be varied with a scroll<br />
bar. The Bernoulli density and p are shown in blue in the first graph; <b<br />
style=""><i style="">p0</i></b> is shown in green. The test statistic<br />
has approximately a standard <span class="GramE"><b style=""><i<br />
style="">N(</i></b></span><b style=""><i style="">μ,σ<sup>2</sup>)</i></b>.<br />
The standard normal density and the critical values are shown in the<br />
second graph in <b style=""><span style="color: blue;">blue</span></b>.<br />
On each update, the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the first graph and<br />
the sample values are recorded in the first table. The sample<br />
proportion <b style=""><i style="">M</i></b> is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the first graph and<br />
the value of the test statistics <b style=""><i style="">Z</i></b> is<br />
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the second graph. The variable I <span class="GramE">indicates</span><br />
the event that the null hypothesis is rejected. On each update, <b<br />
style=""><i style="">M, Z, and I</i></b> are recorded in the second<br />
table. Note that the null hypothesis is reject (I = 1) if and only if<br />
the test statistic Z falls outside of the critical values. Finally, the<br />
empirical density of I is shown in red in the last graph and recorded<br />
in the last table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>QuantileApplet</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">Quantile</span> <span class="SpellE">Applet</span>”<br />
from the list.<span style="">&nbsp; </span><b></b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This applet displays the value (<span<br />
class="SpellE">quantile</span>) x<span class="GramE">&nbsp; and</span><br />
the cumulative probability <b style=""><i style="">p</i></b> = F(x)<br />
for a variety of distributions. The following distributions can be<br />
chosen from the list box:<br><br />
<br><br />
</p><br />
<div style="text-align: center;"><b style=""><i style="">N(μ,σ<sup>2</sup>),<br />
Γ, χ<sup>2</sup>, student t, F, beta, <span class="SpellE">Weibull</span>,<br />
Pareto, logistic, lognormal,</i></b><br><br />
</div><br />
<p class="MsoNormal"> <br><br />
The <span class="SpellE">quantile</span> x and probability <b style=""><i<br />
style="">p</i></b> are shown graphically in terms of either the<br />
probability density function or the cumulative distribution function;<br />
the type of graph can be chosen from a list box. The parameters of the<br />
chosen distribution can be varied with sliders. Enter a new value of x<br />
in the <span class="SpellE">quantile</span> field or a new value of <b<br />
style=""><i style="">p</i></b> in the probability field and then press<br />
Enter to update the display.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Interactive Distributions (<b style="">THIS<br />
APPLET DOES NOT YET WORK)</b></p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>RandomVariableExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">RandomVariableExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment simulates a value of a random<br />
variable with a specified distribution. The value is recorded on each<br />
update. The <span class="GramE"><b style=""><i style="">N(</i></b></span><b<br />
style=""><i style="">μ,σ<sup>2</sup>), Γ, χ<sup>2</sup>, student t, F,<br />
beta, <span class="SpellE">Weibull</span>, Pareto, logistic, and<br />
lognormal distributions</i></b> can be chosen from the list box. In<br />
each case, the parameters of the distribution can be varied with scroll<br />
bars. The density and<br />
moments of the distribution are shown in the distribution graph, and<br />
the moments are given in the distribution table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>RandomWalkExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">RandomWalkExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of tossing <b<br />
style=""><i style="">n</i></b> fair coins. The position of the random<br />
walk after <b style=""><i style="">j</i></b> tosses is the number of<br />
heads minus the number of tails. The random variables of interest are<br />
the final position, the maximum position, the time of the last zero.<br />
The random walk is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the left graph on<br />
each update. The maximum and minimum values are shown as <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> dots on the right<br />
vertical axis; the last zero is shown as a <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> dot on the horizontal<br />
axis. The value of each of the three random variables is recorded in<br />
the first table on each update. Any of the three variables can be<br />
selected from the list box. The density and moments of the selected<br />
variable are shown in blue in the second graph and are recorded in the<br />
second table. On each update, the empirical density and moments are<br />
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the second graph and are recorded in the second table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability, <span class="SpellE">Galton's</span><br />
board game</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>RedBlackExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">RedBlackExperiment</span><b>:</b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">In the red and black experiment, a player<br />
starts with an initial fortune <b style=""><i style="">x</i></b> and<br />
bets (at even stakes) on independent trials for which the probability<br />
of winning is <b style=""><i style="">p</i></b>. Play continues until<br />
the player is either ruined or reaches a fixed target fortune <b<br />
style=""><i style="">a</i></b>.&nbsp; Either of two player strategies<br />
can be selected from a list box. With timid play, the player bets 1 on<br />
each trial. With bold play, the player bets her entire fortune or what<br />
is needed to reach the target (whichever is smaller). Variable <b<br />
style=""><i style="">J</i></b> indicates the event that the player<br />
wins (reaches her target) and variable <b style=""><i style="">N</i></b><br />
is the number of trials played. These variables are recorded on each<br />
update. The first graph shows the initial and target fortunes and the<br />
final outcome. The density of <b style=""><i style="">J</i></b> is<br />
shown in the middle graph and table, and the <b style=""><i style="">μ</i></b><br />
of <b style=""><i style="">N</i></b> is shown in the last graph and<br />
table. The parameters <b style=""><i style="">x and p</i></b> can be<br />
varied with scroll bars, and the target fortune a can be chosen from a<br />
list box.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>RedBlackGame</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
http://www.socr.ucla.edu/htmls/SOCR_Games.html> and<br />
select “<span class="SpellE">RedBlackGame</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_Games.html</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This class models the red-black game.&nbsp;<br />
A player plays Bernoulli trials against the house at even stakes until<br />
she loses her fortune or reaches a specified target fortune.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>RouletteExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">RouletteExperiment</span><b>:</b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The American roulette wheel has 38 slots<br />
numbered 00, 0, and 1-36. Slots 00 and 0 are green. Half of the slots<br />
numbered 1-36 are <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
and half are <b style="">black</b>. The experiment consists of rolling<br />
a ball in a groove in the wheel; the ball eventually falls randomly<br />
into one of the 38 slots. The roulette wheel is shown in the left graph<br />
panel; the ball is shown on each update. One of seven different bets<br />
can be selected from the list box: Bet on 1: this is an example of a<br />
straight bet, and bet pays 35:1. Bet on 1, 2: this is an example of a<br />
split bet, and pays 17:1. Bet on 1, 2, <span class="GramE">3</span>:<br />
this is an example of a row bet, and bet pays 11:1. Bet on 1, 2, 4, <span<br />
class="GramE">5</span>: this is an example of 4-number bet, and pays<br />
8:1. Bet on 1-6: this is an example of a 2-row bet, and pays 5:1. Bet<br />
on 1-12: this is an example of a 12-number bet, and pays 2:1. Bet on<br />
1-18: this is an example of an 18-number bet, and pays 1:1. On each<br />
update, the outcome <b style=""><i style="">X</i></b> is shown<br />
graphically in the first panel and recorded numerically in the first<br />
table. Random variable <b style=""><i style="">W</i></b> gives the net<br />
winnings for the chosen bet; this variable is recorded in the first<br />
table on each update. The density function and moments of <b style=""><i<br />
style="">W</i></b> are shown in <b style=""><span style="color: blue;">blue</span></b><br />
in the distribution graph and are recorded in the distribution table.<br />
On each update, the empirical density and moments of <b style=""><i<br />
style="">W</i></b> are shown in red in the distribution graph and are<br />
recorded in the distribution table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>SampleMeanExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">SampleMeanExperiment</span><b>:</b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This class models the sample mean<br />
experiment. A random sample of a specified size is drawn from a<br />
specified distribution. The <span class="GramE">density of the<br />
sampling distribution and of the distribution of the sample mean are</span><br />
shown.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Random Sampling</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>SignTestExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">SignTestExperiment</span><b>:</b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size n from a distribution, and then to perform a hypothesis test<br />
about the median m of the distribution at a specified significance<br />
level. The distribution can be selected from a list box; the options<br />
are the <span class="GramE"><b style=""><i style="">N(</i></b></span><b<br />
style=""><i style="">μ,σ<sup>2</sup>), Γ, and uniform</i></b><br />
distributions. In each case, the appropriate parameters and the sample<br />
size n can be varied with scroll bars. The significance level can be<br />
selected with a list box. The null hypothesized value <b style=""><i<br />
style="">m0</i></b> of the median can be selected with a scroll bar;<br />
the true <span class="SpellE">quantile</span> level <b style=""><i<br />
style="">p</i></b> of <b style=""><i style="">m0</i></b> is also<br />
given. The density of the distribution and <b style=""><i style="">m</i></b><br />
are shown in <b style=""><span style="color: blue;">blue</span></b> in<br />
the first graph; <b style=""><i style="">m0</i></b> is shown in green.<br />
The test statistic <b style=""><i style="">N</i></b> is the number of<br />
sample values greater than <b style=""><i style="">m0</i></b>. Under<br />
the null hypothesis, <b style=""><i style="">N</i></b> has the<br />
binomial distribution with parameters <b style=""><i style="">n</i></b><br />
and 1/2. The density of this distribution and the critical values are<br />
shown in the second graph in <b style=""><span style="color: blue;">blue</span></b>.<br />
On each update, the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the first graph and<br />
the sample values are recorded in the first table. The value of the<br />
test statistics <b style=""><i style="">N</i></b> is shown in <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b> in the<br />
second graph. The variable <b style=""><i style="">J</i></b> indicates<br />
the event that the null hypothesis is rejected. On each update, <b<br />
style=""><i style="">N and J</i></b> are recorded in the second table.<br />
Note that the null hypothesis is reject (J = 1) if and only if the test<br />
statistic <b style=""><i style="">N</i></b> falls outside of the<br />
critical values. Finally, the empirical density of <b style=""><i<br />
style="">I</i></b> is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the last graph and<br />
recorded in the last table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Hypothesis Test</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>SpinnerExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">SpinnerExperiment</span>” from the<br />
list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists spinning a spinner<br />
and recording the outcome (the sectors are numbered). The number of<br />
sectors in the spinner can be varied with the scroll-bar and the<br />
probability of each sector (which is proportional to the area of the<br />
sector) can be set with the probability dialog. The probability density<br />
function and moments of the random variable (the spinner score) are<br />
shown in <b style=""><span style="color: blue;">blue</span></b> in the<br />
distribution graph and recorded numerically in the distribution table.<br />
When the experiment runs, the empirical density and moments are shown<br />
in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the distribution graph and recorded in the distribution table. In<br />
single step mode, the spinner pointer actually spins, and a sound is<br />
played whose tone depends on the outcome.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>TriangleExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">TriangleExperiment</span><b>:</b></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">Two points are chosen at random in the<br />
interval [0, 1]; <b style=""><i style="">X</i></b> denotes the first<br />
point chosen and <b style=""><i style="">Y</i></b> denotes the second<br />
point chosen. Random variable <b style=""><i style="">U</i></b> gives<br />
the type of triangle that can be formed from the three sub-intervals: U<br />
= 0, the pieces do not form a triangle; U = 1, the pieces form an<br />
obtuse triangle; U = 2, the pieces form an acute triangle. The first<br />
picture box shows the outcome of the experiment graphically. On each<br />
update, the cut points <b style=""><i style="">X and Y</i></b> are<br />
shown as <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
dots, and the triangle is sketched when U = 1 or U = 2. The second<br />
picture box shows the sample space and the three events of interest: U<br />
= 2 <span class="GramE">consists</span> of the 2 interior regions; U =<br />
1 consists of the 6 middle regions; U = 0 consists of the outer<br />
regions. On each run, (X, Y) is shown as a <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> dot in the <span<br />
class="SpellE">scatter plot</span>, and is recorded in the first table<br />
on each update. The probability density function of <b style=""><i<br />
style="">U</i></b> is shown in <b style=""><span style="color: blue;">blue</span></b><br />
in the graph box and is recorded in the graph table. On each update,<br />
the empirical density of <b style=""><i style="">U</i></b> is shown in<br />
<b style=""><span style="color: rgb(255, 102, 0);">red</span></b><span<br />
style="font-weight: bold;"> </span>in the graph box and is recorded<br />
in the graph table. Additionally, the value of <b style=""><i style="">U</i></b><br />
is recorded in the first table on each update.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Calculus Based Probability</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;" valign="top"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>Two<br />
Type Poisson Experiment</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “Two Type Poisson Experiment</span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">” from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">This experiment depicts a two-type <span<br />
class="SpellE">poisson</span> distribution.&nbsp; The theoretical<br />
probabilities of the number of occurrences for each process are<br />
depicted with <b style=""><span style="color: blue;">blue</span></b><br />
histograms, while the observed proportions of the number of occurrences<br />
are displayed using <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
histograms.&nbsp; The theoretical and observed <b style=""><i style="">μ,<br />
σ, and proportions</i></b> of the second process (the graph on the<br />
right side of the screen) <span class="GramE">is</span> illustrated in<br />
the right third of the green space.&nbsp; The theoretical and observed <b<br />
style=""><i style="">μ, σ, and proportions</i></b> of the first<br />
process (the graph on the left side of the screen) <span class="GramE">is</span><br />
illustrated in the middle third of the green space.&nbsp; The results<br />
of each experiment are depicted in the left third of the green space. </p><br />
</td><br />
<td<br />
style="padding: 1.5pt; text-align: center; vertical-align: middle;"><br />
<p class="MsoNormal">Two type Poisson Distribution</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>UniformEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">UniformEstimateExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment<br />
is to generate a random sample X<span class="SpellE"><sub>1</sub></span>,<br />
X<span class="SpellE"><sub>2</sub></span>, ..., <span class="SpellE">X</span><span<br />
class="SpellE"><sub>n</sub></span> of size <b style=""><i style="">n</i></b><br />
from the uniform distribution on (0, <b style=""><i style="">a</i></b>).<br />
The distribution density is shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the graph, and on each update,<br />
the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. On each update, the<br />
following statistics are recorded: </p><br />
<p style="text-align: center;" class="MsoNormal">U<br />
= 2M where M = (X<span class="SpellE"><sub>1</sub></span> + X<span<br />
class="SpellE"><sub>2</sub></span> + ••• + <span class="SpellE">X</span><span<br />
class="SpellE"></span><span class="SpellE"><sub>n</sub></span>) / n <br><br />
(the sample mean)<br><br />
V = (n + 1)X(n) / n where X(n) = max{X<span class="SpellE"><sub>1</sub></span>,<br />
X<span class="SpellE"><sub>2</sub></span>, ..., <span class="SpellE">X</span><span<br />
class="SpellE"><sub>n</sub></span><span class="SpellE"></span>} <br><br />
(the <span class="SpellE">n'th</span> order statistic)<br><br />
W = (n + 1)X(1) where X(1) = min{X<span class="SpellE"><sub>1</sub></span>,<br />
X<span class="SpellE"><sub>2</sub></span>, ..., <span class="SpellE">X</span><span<br />
class="SpellE"><sub>n</sub></span>} <br><br />
(the first order statistic)</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>UrnExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">UrnExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment consists of selecting <b<br />
style=""><i style="">n</i></b> balls at random from an urn with <b<br />
style=""><i style="">N</i></b> balls, <b style=""><i style="">R</i></b><br />
of which are <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
and the other N - R <b style=""><span style="color: green;">green</span></b>.<br />
The number of <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
balls Y in the sample is recorded on each update. The distribution and<br />
moments of <b style=""><i style="">Y</i></b> are shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the distribution graph and are<br />
recorded in the distribution table. On each update, the empirical<br />
density and moments of <b style=""><i style="">Y</i></b> are shown in <b<br />
style=""><span style="color: rgb(255, 102, 0);">red</span></b> in the<br />
distribution graph and are recorded in the distribution table. Either<br />
of two sampling models can be selected with the list box: with<br />
replacement and without replacement. The parameters <b style=""><i<br />
style="">N, R, and n</i></b> can be varied with scroll bars.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">Demos of <span class="SpellE"><b>Hypergeometric</b></span><b><br />
</b>and <b>Binomial </b>Distributions. As well as the<br />
approximation of <span class="SpellE">hypergeometric</span> by (the<br />
simpler) binomial when the sample-size &lt; 5-10% of the population<br />
size.</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>VarianceEstimateExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">VarianceEstimateExperiment</span>”<br />
from the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size <b style=""><i style="">n</i></b> from a specified<br />
distribution, and then to construct an approximate confidence interval<br />
for <b style=""><i style="">σ</i></b> at a specified confidence level.<br />
The distribution can be chosen with a list box; the options are <span<br />
class="GramE"><b style=""><i style="">N(</i></b></span><b style=""><i<br />
style="">μ,σ<sup>2</sup>), Γ, and uniform</i></b>. In each case, the<br />
appropriate parameters and the sample size can be varied with scroll<br />
bars. The density, <b style=""><i style="">μ</i></b>, and <span<br />
class="GramE"><b style=""><i style="">σ</i></b> <span style="">&nbsp;</span>of</span><br />
the selected distribution are shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the first graph. The<br />
confidence level can be selected from a list box, as can the type of<br />
interval--two sided, upper bound, or lower bound. The interval can be<br />
constructed assuming either that the distribution mean <b style=""><i<br />
style="">μ</i></b> is known or unknown. In the first case the pivot<br />
variable <b style=""><i style="">V</i></b> has the <b style=""><i<br />
style="">χ<sup>2</sup></i></b><sup> </sup>distribution with n degrees<br />
of freedom; in the second case the pivot variable <b style=""><i<br />
style="">V</i></b> has <b style=""><i style="">χ<sup>2</sup></i></b><sup><br />
</sup>distribution with n - <span class="GramE">1 degrees of<br />
freedom</span>. The density and the critical values of V are shown in<br />
blue in the second graph. Variables <b style=""><i style="">L and R</i></b><br />
<span class="GramE">denote</span> the left and right endpoints of<br />
the confidence interval and <b style=""><i style="">I</i></b><br />
indicates the event that the confidence interval contains the<br />
distribution mean. The theoretical density of <b style=""><i style="">I</i></b><br />
is shown in <b style=""><span style="color: blue;">blue</span></b> in<br />
the third graph. On each update, the sample density and the confidence<br />
interval are shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the first graph,<br />
and the value of <b style=""><i style="">V</i></b> is shown in red in<br />
the second graph. Note that the confidence interval contains the mean<br />
in the first graph if and only if <b style=""><i style="">V</i></b><br />
falls between the critical values in the second graph. The third graph<br />
shows the proportion of successes and failures in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b>. The first table gives<br />
the sample values; the second table records <b style=""><i style="">L,<br />
R, V, and I.</i></b> Finally, the third table gives the <span<br />
class="SpellE">theoretical</span> and empirical densities of <b<br />
style=""><i style="">I.</i></b></p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>VarianceTestExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">VarianceTestExperiment</span>” from<br />
the list.<span style="">&nbsp; </span></span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><b>&nbsp;</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">The experiment is to select a random sample<br />
of size <b style=""><i style="">n</i></b> from a selected distribution<br />
and then test a hypothesis about the standard deviation <b style=""><i<br />
style="">d</i></b> at a specified significance level. The distribution<br />
can be selected from a list box; the options are the <span<br />
class="GramE"><b style=""><i style="">N(</i></b></span><b style=""><i<br />
style="">μ,σ<sup>2</sup>), Γ, and uniform</i></b> distributions. In<br />
each case, the appropriate parameters and the sample size n can be<br />
varied with scroll bars.&nbsp; The significance level can be selected<br />
with a list box, as can the type of test: two-sided, left-sided, or<br />
right-sided. The boundary point <b style=""><i style="">d0</i></b><br />
between the null and alternative hypotheses can be varied with a scroll<br />
bar. The density of the distribution, as well as <b style=""><i<br />
style="">m and d</i></b>, are shown in <b style=""><span<br />
style="color: blue;">blue</span></b> in the first graph; <b style="">d0<br />
</b>is shown in <b style=""><span style="color: green;">green</span></b>.<br />
The test can be constructed under the assumption that the distribution<br />
mean is known or unknown. In the first case, the test statistic has the<br />
<b style=""><i style="">χ<sup>2 </sup></i></b>distribution with<br />
n degrees of freedom; in the second case the test statistics has the <b<br />
style=""><i style="">χ<sup>2</sup></i></b><sup> </sup>distribution<br />
with n - <span class="GramE">1 degrees of freedom</span>. The density<br />
and the critical values of the test statistic <b style=""><i style="">V</i></b><br />
are shown in the second graph in <b style=""><span style="color: blue;">blue</span></b>.&nbsp;<br />
On each update, the sample density is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the first graph and<br />
the sample values are recorded in the first table. The sample standard<br />
deviation <b style=""><i style="">S</i></b> is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the first graph and<br />
the value of the test statistic <b style=""><i style="">V</i></b> is<br />
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b><br />
in the second graph. The variable I <span class="GramE">indicates</span><br />
the event that the null hypothesis is rejected. On each update, <b<br />
style=""><i style="">S<sup>2</sup>, V, and I</i></b> are recorded in<br />
the second table. Note that the null hypothesis is reject (I = 1) if<br />
and only if the test statistic <b style=""><i style="">V</i></b> falls<br />
outside of the critical values. Finally, the empirical density of <b<br />
style=""><i style="">I</i></b> is shown in <b style=""><span<br />
style="color: rgb(255, 102, 0);">red</span></b> in the last graph and<br />
recorded in the last table.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
<tr style=""><br />
<td style="padding: 1.5pt; width: 25%;"><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
class="SpellE"><b>VoterExperiment</b></span><b>:</b></p><br />
<p class="MsoNormal" style="text-align: center;" align="center"><span<br />
style="">To view this experiment, click <br />
[http://www.socr.ucla.edu/htmls/SOCR_Experiments.html here]<br />
and select “<span class="SpellE">VoterExperiment</span>” from the list.<span<br />
style="">&nbsp; </span></span></p><br />
<p class="MsoNormal"><span style="">&nbsp;</span></p><br />
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p><br />
<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; vertical-align: middle; text-align: justify;"><br />
<p class="MsoNormal">Each site in the voter array can be in one<br />
of 10 states, represented by various colors. At each discrete time<br />
unit, a site is chosen at random, and then a neighbor of the site is<br />
chosen at random. The state (color) of the site is changed to the state<br />
(color) of the neighbor.&nbsp; The record table shows the number of<br />
sites of each color on each update. You can change the state of a site<br />
by selecting the desired color in the list box and then clicking on the<br />
desired site.</p><br />
</td><br />
<td<br />
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"<br />
width="25%"><br />
<p class="MsoNormal">&nbsp;</p><br />
</td><br />
</tr><br />
</table></div>IvoDinov