http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&feed=atom&action=historySOCR EduMaterials Activities JointDistributions - Revision history2024-03-28T19:57:38ZRevision history for this page on the wikiMediaWiki 1.15.1http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2468&oldid=prevIvoDinov at 03:12, 29 December 20062006-12-29T03:12:05Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2362&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:25:30Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Below you can see a snapshot of the theoretical distribution of <math> Y </math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Below you can see a snapshot of the theoretical distribution of <math> Y </math>.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Below you can see a snapshot of the theoretical distribution of <math> Y </math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Below you can see a snapshot of the theoretical distribution of <math> Y </math>.</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2361&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:20:01Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to explore the joint distributions of X and Y through two simple examples. ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to explore the joint distributions of X and Y through two simple examples. ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>* '''Description''': You can access the applets for the <del class="diffchange diffchange-inline">folowing </del>experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* '''Description''': You can access the applets for the <ins class="diffchange diffchange-inline">following </ins>experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2360&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:19:18Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>A die is rolled and the number observed <math> X </math> is recorded. Then a coin is tossed number of times equal to the value of <math>X</math<del class="diffchange diffchange-inline">?</del>. For example if <math>X=2</math> then the coin is tossed twice, etc. Let <math>Y</math> be the number of heads observed. Note: Assume that the die and the coin are fair.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>A die is rolled and the number observed <math> X </math> is recorded. Then a coin is tossed number of times equal to the value of <math>X</math<ins class="diffchange diffchange-inline">></ins>. For example if <math>X=2</math> then the coin is tossed twice, etc. Let <math>Y</math> be the number of heads observed. Note: Assume that the die and the coin are fair.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>**'''1.''' Construct the joint probability distribution of <math>X</math> and <math>Y</math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>**'''1.''' Construct the joint probability distribution of <math>X</math> and <math>Y</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>**'''2.''' Find the conditional expected value of <math>Y</math> given <math>X=5</math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>**'''2.''' Find the conditional expected value of <math>Y</math> given <math>X=5</math>.</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2359&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:18:08Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to explore the joint distributions of X and Y through two simple examples. ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to explore the joint distributions of X and Y through two simple examples. ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>* '''Description''': You can access the applets for the folowing experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html <del class="diffchange diffchange-inline">Exponential Distributions</del>] </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>* '''Description''': You can access the applets for the folowing experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html <ins class="diffchange diffchange-inline">SOCR Experiments</ins>] </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2358&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:17:34Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to explore the joint distributions of X and Y through two simple examples. ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to explore the joint distributions of X and Y through two simple examples. ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>You can access the <del class="diffchange diffchange-inline">following </del>experiments <del class="diffchange diffchange-inline">in SOCR under Experiments</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">* '''Description''': </ins>You can access the <ins class="diffchange diffchange-inline">applets for the folowing </ins>experiments <ins class="diffchange diffchange-inline">at [http://www.socr.ucla.edu/htmls/SOCR_Experiments</ins>.<ins class="diffchange diffchange-inline">html Exponential Distributions] </ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* '''Exercise 1''': Die coin experiment:</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2357&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:14:45Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2356&oldid=prevNchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */2006-11-25T05:14:20Z<p><span class="autocomment">This is an activity to explore the joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* SOCR Home page: http://www.socr.ucla.edu</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2355&oldid=prevNchristo: /* This is an activity to explore he joint distributions of X and Y through two simple examples. */2006-11-25T05:12:54Z<p><span class="autocomment">This is an activity to explore he joint distributions of X and Y through two simple examples.</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>== This is an activity to explore <del class="diffchange diffchange-inline">he </del>joint distributions of X and Y through two simple examples. ==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>== This is an activity to explore <ins class="diffchange diffchange-inline">the </ins>joint distributions of X and Y through two simple examples. ==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can access the following experiments in SOCR under Experiments.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can access the following experiments in SOCR under Experiments.</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_JointDistributions&diff=2354&oldid=prevNchristo at 05:11, 25 November 20062006-11-25T05:11:59Z<p></p>
<p><b>New page</b></p><div>== This is an activity to explore he joint distributions of X and Y through two simple examples. ==<br />
<br />
You can access the following experiments in SOCR under Experiments.<br />
<br />
* '''Exercise 1''': Die coin experiment:<br />
A die is rolled and the number observed <math> X </math> is recorded. Then a coin is tossed number of times equal to the value of <math>X</math?. For example if <math>X=2</math> then the coin is tossed twice, etc. Let <math>Y</math> be the number of heads observed. Note: Assume that the die and the coin are fair.<br />
**'''1.''' Construct the joint probability distribution of <math>X</math> and <math>Y</math>.<br />
**'''2.''' Find the conditional expected value of <math>Y</math> given <math>X=5</math>.<br />
**'''3.''' Find the conditional variance of <math>Y</math> given <math>X=5</math>.<br />
**'''4.''' Find the expected value of <math>Y</math>.<br />
**'''5.''' Find the standard deviation of <math>Y</math>.<br />
**'''6.''' Graph the probability distribution of <math>Y</math>.<br />
**'''7.''' Use SOCR to graph and print the empirical distribution of <math>Y</math> when the experiment is performed <br />
***'''a.''' <math>n=1000</math> times.<br />
***'''b.''' <math>n=10000</math> times.<br />
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**'''8.''' Compare the theoretical mean and standard deviation of <math>Y</math> (parts (4) and (5)) with the empirical mean and standard deviation found in part (8).<br />
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Below you can see a snapshot of the theoretical distribution of <math> Y </math>.<br />
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* '''Exercise 2''': Coin Die experiment:<br />
A coin is tossed and if heads is observed then a red die is rolled. If tails is observed then a green die is rolled. You can choose the distribution of each die as well as the probability of heads. Choose for the red die the 3-4 flat distribution and for the green die the skewed right distribution. Finally using the scroll button choose $p=0.2$ as the probability of heads. Let <math>X</math> be the score of the coin (1 for heads, 0 for tails), and let <math>Y</math> be the score of the die (1,2,3,4,5,6).<br />
**'''1.''' Construct the joint probability distribution of <math>X, Y</math>.<br />
**'''2.''' Find the marginal probability distribution of <math>Y</math> and verify that it is the same with the one given in the applet.<br />
**'''3.''' Compute <math>E(Y)</math>.<br />
**'''4.''' Compute <math>E(Y)</math> using expectation by conditioning <math>E[E(Y|X)]</math>. <br />
**'''5.''' Run the experiment 1000 times take a snapshot and comment on the results.<br />
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Below you can see a snapshot of the theoretical distribution of <math> Y </math>.<br />
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* SOCR Home page: http://www.socr.ucla.edu<br />
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