http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&feed=atom&action=historySOCR EduMaterials Activities MontyHall - Revision history2024-03-29T02:30:03ZRevision history for this page on the wikiMediaWiki 1.15.1http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=6350&oldid=prevIvoDinov at 23:46, 8 February 20082008-02-08T23:46:42Z<p></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 find the probability of winning the Let's Make a Deal (Monty Hall) experiment. ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">Open </del>http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and <del class="diffchange diffchange-inline">use the scroll bar to find </del>the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. Below you can see the result of a single run of the experiment.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Go to the [</ins>http://www.socr.ucla.edu/htmls/SOCR_Experiments.html <ins class="diffchange diffchange-inline">SOCR Experiments] </ins>and <ins class="diffchange diffchange-inline">select </ins>the <ins class="diffchange diffchange-inline">'''</ins>Monty Hall Experiment<ins class="diffchange diffchange-inline">''' from the drop-down list of experiments on the top-left</ins>. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. Below you can see the result of a single run of the experiment<ins class="diffchange diffchange-inline">. You can also play the [http://socr.ucla.edu/htmls/SOCR_Games.html Interactive Manty Hall Game]</ins>.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image: SOCR_Activities_Monty_Hall_Christou_Monty_Hall.jpg|600px]]</center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image: SOCR_Activities_Monty_Hall_Christou_Monty_Hall.jpg|600px]]</center></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Answer the following questions:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Answer the following questions:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''a.''' There are three random variables (<math> G, S, W </math>) and one parameter (<math> p </math>) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''a.''' There are three random variables (<math> G, S, W </math>) and one parameter (<math> p </math>) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).</div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2464&oldid=prevIvoDinov at 03:02, 29 December 20062006-12-29T03:02:56Z<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_MontyHall&diff=2227&oldid=prevNchristo: /* This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. */2006-10-20T21:45:34Z<p><span class="autocomment">This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''i.''' Reset and change <math>p=0.5 </math>, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of <math> W </math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''i.''' Reset and change <math>p=0.5 </math>, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of <math> W </math>.</div></td></tr>
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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_MontyHall&diff=2224&oldid=prevNchristo: /* This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. */2006-10-20T21:00:35Z<p><span class="autocomment">This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''i.''' Reset and change <math>p=0.5 </math>, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of <math> W </math>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''i.''' Reset and change <math>p=0.5 </math>, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of <math> W </math>.</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;">* SOCR Home page: http://www.socr.ucla.edu</ins></div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2194&oldid=prevNchristo: /* This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. */2006-10-20T00:01:11Z<p><span class="autocomment">This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.</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 find the probability of winning the Let's Make a Deal (Monty Hall) experiment. ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. ==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. <del class="diffchange diffchange-inline"> </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. <ins class="diffchange diffchange-inline"> Below you can see the result of a single run of the experiment.</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image: SOCR_Activities_Monty_Hall_Christou_Monty_Hall.jpg|600px]]</center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center>[[Image: SOCR_Activities_Monty_Hall_Christou_Monty_Hall.jpg|600px]]</center></div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2193&oldid=prevNchristo: /* This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. */2006-10-19T23:59:45Z<p><span class="autocomment">This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. </div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2192&oldid=prevNchristo: /* This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. */2006-10-19T23:59:16Z<p><span class="autocomment">This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.</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 find the probability of winning the Let's Make a Deal (Monty Hall) experiment. ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. Answer the following questions:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <I> standard </I> version of the game, which is the default setting of the applet. </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>Answer the following questions:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''a.''' There are three random variables (<math> G, S, W </math>) and one parameter (<math> p </math>) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''a.''' There are three random variables (<math> G, S, W </math>) and one parameter (<math> p </math>) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2190&oldid=prevNchristo: /* This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. */2006-10-19T23:50:05Z<p><span class="autocomment">This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''f.''' Using the three snapshots just taken, compare the theoretical probability distribution of <math> W </math> with the empirical distribution.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''f.''' Using the three snapshots just taken, compare the theoretical probability distribution of <math> W </math> with the empirical distribution.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''g.''' For the three snapshots taken, look at the graph on the bottom right hand corner, and compare the blue lines with the shaded red area. Where does the graph come from and how do they relate to the part (f)?</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''g.''' For the three snapshots taken, look at the graph on the bottom right hand corner, and compare the blue lines with the shaded red area. Where does the graph come from and how do they relate to the part (f)?</div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2189&oldid=prevNchristo: /* This activity */2006-10-19T23:49:34Z<p><span class="autocomment">This activity</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>==This activity==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>== This <ins class="diffchange diffchange-inline">is an </ins>activity <ins class="diffchange diffchange-inline">to find the probability of winning the Let's Make a Deal (Monty Hall) experiment. </ins>==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\noindent </del>Open <del class="diffchange diffchange-inline">$</del>http://www.socr.ucla.edu/htmls/<del class="diffchange diffchange-inline">SOCR\_Experiments</del>.html<del class="diffchange diffchange-inline">$ </del>and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <del class="diffchange diffchange-inline">{\it </del>standard<del class="diffchange diffchange-inline">} </del>version of the game, which is the default setting of the applet. Answer the following questions:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Open http://www.socr.ucla.edu/htmls/<ins class="diffchange diffchange-inline">SOCR_Experiments</ins>.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the <ins class="diffchange diffchange-inline"><I> </ins>standard <ins class="diffchange diffchange-inline"></I> </ins>version of the game, which is the default setting of the applet. Answer the following questions:</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\begin{itemize}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[a.] There are three random variables ($G, S, W$) and one parameter ($p$) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[b.] Run the experiment just once (make sure $p=1$, which means the player always switches), make a snapshot of the outcome, and describe what happened (i.e. What door did the player chose at first? Which door did the host opened? Did the player switch? Did the player win?).</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[c.] Perform 10 runs, take a snapshot.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[d</del>.<del class="diffchange diffchange-inline">] </del> <del class="diffchange diffchange-inline">Reset and perform 100 runs</del>, take a <del class="diffchange diffchange-inline">snapshot</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''a</ins>.<ins class="diffchange diffchange-inline">''' </ins> <ins class="diffchange diffchange-inline">There are three random variables (<math> G</ins>, <ins class="diffchange diffchange-inline">S, W </math>) and one parameter (<math> p </math>) involved in this experiment. Describe what each one represents and what possible values they can </ins>take <ins class="diffchange diffchange-inline">(you find it helpful if you run the experiment </ins>a <ins class="diffchange diffchange-inline">few times before you answer the question)</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[e</del>.<del class="diffchange diffchange-inline">] </del> <del class="diffchange diffchange-inline">Reset and perform 1000 runs</del>, <del class="diffchange diffchange-inline">take </del>a snapshot.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''b</ins>.<ins class="diffchange diffchange-inline">''' </ins> <ins class="diffchange diffchange-inline">Run the experiment just once (make sure <math> p=1 </math></ins>, <ins class="diffchange diffchange-inline">which means the player always switches), make </ins>a snapshot <ins class="diffchange diffchange-inline">of the outcome, and describe what happened (i.e. What door did the player chose at first? Which door did the host opened? Did the player switch? Did the player win?)</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[f</del>.<del class="diffchange diffchange-inline">] </del> <del class="diffchange diffchange-inline">Using the three snapshots just taken</del>, <del class="diffchange diffchange-inline">compare the theoretical probability distribution of $W$ with the empirical distribution</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''c</ins>.<ins class="diffchange diffchange-inline">''' </ins> <ins class="diffchange diffchange-inline">Perform 10 runs</ins>, <ins class="diffchange diffchange-inline">take a snapshot</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></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;">'''d.''' Reset and perform 100 runs, take a snapshot.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[g</del>.<del class="diffchange diffchange-inline">] </del> <del class="diffchange diffchange-inline">For the three snapshots taken</del>, <del class="diffchange diffchange-inline">look at the graph on the bottom right hand corner, and compare the blue lines with the shaded red area</del>. <del class="diffchange diffchange-inline"> Where does the graph come from and how do they relate to the part (f)?</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''e</ins>.<ins class="diffchange diffchange-inline">''' </ins> <ins class="diffchange diffchange-inline">Reset and perform 1000 runs</ins>, <ins class="diffchange diffchange-inline">take a snapshot</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\item[h</del>.<del class="diffchange diffchange-inline">] Reset and change $p=0$</del>, <del class="diffchange diffchange-inline">which means the player never switches. Perform 100 runs and take a snapshot. Describe </del>the theoretical <del class="diffchange diffchange-inline">and empirical </del>distribution of <del class="diffchange diffchange-inline">$</del>W<del class="diffchange diffchange-inline">$</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''f</ins>.<ins class="diffchange diffchange-inline">''' Using the three snapshots just taken</ins>, <ins class="diffchange diffchange-inline">compare </ins>the theoretical <ins class="diffchange diffchange-inline">probability </ins>distribution of <ins class="diffchange diffchange-inline"><math> </ins>W <ins class="diffchange diffchange-inline"></math> with the empirical distribution</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></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;">\item[i.] Reset and change $p=0.5$, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of $W$.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></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;">'''g.''' For the three snapshots taken, look at the graph on the bottom right hand corner, and compare the blue lines with the shaded red area. Where does the graph come from and how do they relate to the part (f)?</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></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;">'''h.''' Reset and change <math> p=0 </math>, which means the player never switches. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of <math> W </math>.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">\end{itemize}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''i.''' Reset and change <math>p=0.5 </math>, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of <math> W </math>.</ins></div></td></tr>
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</table>Nchristohttp://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_MontyHall&diff=2188&oldid=prevNchristo at 23:40, 19 October 20062006-10-19T23:40:00Z<p></p>
<p><b>New page</b></p><div>==This activity==<br />
<br />
\noindent Open $http://www.socr.ucla.edu/htmls/SOCR\_Experiments.html$ and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the {\it standard} version of the game, which is the default setting of the applet. Answer the following questions:<br />
\begin{itemize}<br />
\item[a.] There are three random variables ($G, S, W$) and one parameter ($p$) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).<br />
\item[b.] Run the experiment just once (make sure $p=1$, which means the player always switches), make a snapshot of the outcome, and describe what happened (i.e. What door did the player chose at first? Which door did the host opened? Did the player switch? Did the player win?).<br />
\item[c.] Perform 10 runs, take a snapshot.<br />
<br />
\item[d.] Reset and perform 100 runs, take a snapshot.<br />
<br />
\item[e.] Reset and perform 1000 runs, take a snapshot.<br />
<br />
\item[f.] Using the three snapshots just taken, compare the theoretical probability distribution of $W$ with the empirical distribution.<br />
<br />
<br />
\item[g.] For the three snapshots taken, look at the graph on the bottom right hand corner, and compare the blue lines with the shaded red area. Where does the graph come from and how do they relate to the part (f)?<br />
<br />
\item[h.] Reset and change $p=0$, which means the player never switches. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of $W$.<br />
<br />
\item[i.] Reset and change $p=0.5$, which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of $W$.<br />
<br />
<br />
<br />
\end{itemize}</div>Nchristo