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SOCR_InstructorPlan.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>SOCR: Statistics Online Computational Resource</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="description"
content="Statistics Online Computational Resource">
<meta name="keywords"
content="Statistics Online Computational Resource">
<meta name="author" content="Ivo Dinov: www.SOCR.ucla.edu">
<link rel="stylesheet" type="text/css" href="../htmls/SOCRstyle.css">
<link rel="shortcut icon" href="../SOCR_Web_Icon.ico">
<script language="JavaScript"
src="http://www.gvisit.com/record.php?sid=d99391579a14b519d3e195107a1706bf"
type="text/javascript"></script>
<script src="http://www.google-analytics.com/urchin.js"
type="text/javascript"> </script>
<script type="text/javascript"> _uacct = "UA-676559-1"; urchinTracker(); </script>
</head>
<body>
<div id="wrapper-menu-top">
<div id="menu-top">
<ul>
<li><a href="../SOCR.html" title="SOCR Home"><span>SOCR Home</span></a></li>
<li><span> Tools ⇒ </span></li>
<li><a href="SOCR_Distributions.html" title="SOCR Distributions"><span>Distributions</span></a></li>
<li><a href="SOCR_Experiments.html" title="SOCR Experiments & Demos"><span>Experiments</span></a></li>
<li><a href="SOCR_Analyses.html" title="SOCR Analyses"><span>Analyses</span></a></li>
<li><a href="SOCR_Games.html" title="SOCR Games"><span>Games</span></a></li>
<li><a href="SOCR_Modeler.html" title="SOCR Modeler"><span>Modeler</span></a></li>
<li><a href="SOCR_Charts.html" title="SOCR Charts"><span>Charts</span></a></li>
<li><a href="../Applets.dir/OnlineResources.html"
title="Additional Resources"><span>More</span></a></li>
</ul>
</div>
<!--menu-top--></div>
<!--wrapper-menu-top-->
<div id="wrapper-header">
<div id="header">
<div id="wrapper-header2">
<div id="wrapper-header3">
<h1>
<center>SOCR Instructor Plans<br>
</center>
</h1>
</div>
</div>
</div>
</div>
<div id="wrapper-content">
<div id="wrapper-menu-page">
<div id="menu-page">
<h3><u>Interactive SOCR Tools</u></h3>
<ul>
<li><a href="SOCR_Distributions.html">SOCR Distributions</a></li>
<li><a href="SOCR_Experiments.html">SOCR Experiments</a></li>
<li><a href="SOCR_Analyses.html">SOCR Analyses</a></li>
<li><a href="SOCR_Games.html">SOCR Games</a></li>
<li><a href="SOCR_Modeler.html">SOCR Data Modeler</a></li>
<li><a href="SOCR_Charts.html">SOCR Plots & Charts</a></li>
<li><a href="../Applets.dir/OnlineResources.html">Additional SOCR
Resources</a></li>
</ul>
<h3><u>SOCR Resources</u></h3>
<ul>
<li><a href="SOCR_About.html">About</a></li>
<li><a
href="http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials">Courses
& Educational Materials</a></li>
<li><a href="../docs/SOCR_Documentation.html">Documentation</a></li>
<li><a href="SOCR_Download.html">Download</a></li>
<li><a href="http://moodle.stat.ucla.edu/mod/forum/view.php?f=20">Forum</a></li>
</ul>
</div>
<!--menu-page--></div>
<div id="content">
<h2 style="text-decoration: underline;">SOCR Pedagorical Utilization
Resources<br>
</h2>
<p><img title="SOCR Resource"
src="http://www.socr.ucla.edu/images.dir/SOCR_Logo.gif" alt="SOCR Logo"
style="width: 180px; height: 132px;" align="right" hspace="5"
vspace="5"></p>
<p class="MsoNormal"><o:p> <br>
</o:p></p>
<p class="MsoNormal"><o:p><br>
<br>
</o:p></p>
<table class="MsoNormalTable" style="width: 100%;" border="1"
cellpadding="0">
<tbody>
<tr style="">
<td
style="padding: 1.5pt; text-align: center; vertical-align: middle; width: 25%;">
<p class="MsoNormal"
style="margin-bottom: 12pt; text-align: center;" align="center"><u><br>
EXPERIMENTS</u></p>
</td>
<td
style="padding: 1.5pt; text-align: center; vertical-align: middle;">
<p class="MsoNormal"><u><br>
</u></p>
<div style="text-align: center;"><u>DESCRIPTION</u></div>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><u><br>
APPLICATIONS</u></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;" valign="top">
<p class="MsoNormal" style="text-align: center;" align="center"><b>Ball
and Urn Experiment<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “Ball and Urn Experiment” from the list.<span style="">
</span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">This experiment exemplifies the
binomial distribution. The user determines the parameters of the
binomial distribution (<span class="SpellE"><b style="">n<span
class="GramE">,p,k</span></b></span>), and the computer randomly
choose balls according to that distribution. The red ball is
considered a “success”, while the green ball is considered the
“failure”. The blue histogram displays the probabilities of
choosing all possible numbers of red balls, while the red histogram
displays the observed proportions of the cumulative number of red balls
chosen per trial. The theoretical and observed μ and σ are
displayed beneath the histograms. The numerical probabilities and
observed proportions of each result are also given. </p>
</td>
<td
style="padding: 1.5pt; text-align: center; vertical-align: middle;">
<p class="MsoNormal">Binomial Distribution</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BallotExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BallotExperiment</span>:<b><o:p></o:p></b></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">” from the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><b
style=""><o:p> </o:p></b></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">In an election, candidate A receives <span
style="font-weight: bold;">a</span> votes and candidate B receives <span
style="font-weight: bold;">b</span> votes, where <b>a > b</b>. The
votes are assumed to be randomly ordered. The first graph shows the
difference between the number of votes for A and the <span
class="GramE">number of votes for B, as the votes are</span> counted. <b>The
event of interest is that A is always ahead of B in the vote count, or
equivalently, that the graph is always above the horizontal axis</b>
(except of course at the origin). The <i>indicator variable I of this
event is recorded in the first table</i> on each update. The density
function of I is shown in blue in the second graph and is recorded in
the second table. On each update, the empirical density of I is shown
as red in the second graph and recorded in the second table. The
parameters <span class="GramE"><span style="font-weight: bold;">a</span>
and</span> <span style="font-weight: bold;">b</span> can be varied
with scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><o:p> </o:p></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BertrandExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BertrandExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">Bertrand's experiment is to generate a
random chord of a circle. In the <span class="SpellE">simulation, one</span>
point of the chord is fixed at (1, 0) and the other random point (X, Y)
is recorded on each update in the first table. Also recorded are <u>D,
the length of the line <span class="SpellE">segment from</span> the
center of the circle to the center of the chord</u>, and <u>A, the
angle that this <span class="SpellE">line segment</span> makes with
the horizontal</u>. Variable <b><i style="">I</i> <span class="GramE">indicates</span>
the event that the chord is longer than the length of a side of the
inscribed equilateral triangle</b>. The density of I is shown in blue
in the distribution graph and <span class="SpellE">and</span> is
recorded in the distribution table. On each update, the empirical
density of I is shown in red in the distribution graph and is recorded
in the distribution table. Three different models can be selected with
the list box: the model where the distance D is uniformly distributed,
the model where the angle A is uniformly distributed, and the model
where the coordinate X is uniformly distributed.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><o:p> </o:p></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BetaCoinExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BetaCoinExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment is to toss <span
class="GramE">a coin n times</span>, where the probability of heads is
p. The <b>probability of heads is modeled with a prior </b><b style=""><i
style="">β</i></b><i style=""> <b>distribution</b></i>, having
parameters <span class="GramE"><b><i style="">a</i> </b>and</span> <b><i
style="">b</i></b>. The prior density and the true probability of
heads are shown in blue in the graph on the right. On each update, the
number of heads Y is recorded in the first table. On each update, the <b>posterior
</b>β <b>density, which has parameters a + Y and b + n - Y is
shown in <span style="color: rgb(255, 102, 0);">red</span> in graph on
the right</b>. Also, the <b>Bayesian estimate of p, U = (a + Y) / (a +
b + n)</b> is recorded in the first table on each update. Finally, the
second table gives the true <span class="SpellE">distBias</span> and
mean square error of <span class="GramE">U,</span> and on each update
gives the empirical <span class="SpellE">distBias</span> and mean
square error, based on the all of the runs of the experiment. The
parameters <b style=""><i style="">n, p, a,</i> </b>and<b style=""> <i
style="">b</i></b> can be varied with scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Bayesian Estimation - Prior/Posterior.</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BetaEstimateExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BetaEstimateExperiment</span>” from
the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment
is to generate a random sample X<sub>1</sub>, X<sub>2</sub>, ..., <span
class="SpellE">X</span><sub>n</sub> of size n from the <b style="">β <span
style="">distribution with parameters a and 1</span></b>. The
distribution density is shown in blue in the graph, and on each update,
the sample density is shown in <b style=""><span
style="color: rgb(255, 102, 0);">red</span></b>. On each update, the
following statistics are recorded: </p>
<p style="text-align: center;" class="MsoNormal">U
= M / (1 - M) where M = (X<sub>1</sub> + X<sub>2</sub> + ··· + <span
class="SpellE">X</span><sub>n</sub>) / n<br>
V = -n / [<span class="SpellE">ln</span>(X<sub>1</sub>) + <span
class="SpellE">ln</span>(X<sub>2</sub>) + ··· + <span class="SpellE"><span
class="GramE">ln</span></span><span class="GramE">(</span><span
class="SpellE">X</span><sub>n</sub>)]. </p>
<p class="MsoNormal"><br>
Statistics<u> U and V are point estimators of <b>a</b></u>. As the
experiment runs, the empirical bias and mean square error of each
estimator are recorded in the second table. The parameters a and n can
be varied with scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Bias & precision in parameter
estimation, using Beta-distribution.</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BinomialCoinExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BinomialCoinExperiment</span>” from
the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment consists of tossing n <span
class="GramE">coins,</span> each with probability of heads <span
class="SpellE"><b style="">p. The</b></span> <b style="">number of
heads X</b> and the <b style="">proportion of heads M</b> are recorded
on each <span class="SpellE">update. Either</span> <b style="">X</b>
or <b style="">M</b> can be selected with the list box. The discrete
probability density function and moments of the selected variable are
shown in blue in the distribution graph and are recorded in the
distribution table. On each update, the empirical probability density
function and moments of the selected variable are shown in red in the
distribution graph and are recorded in the distribution table. The
parameters <b style="">n</b> and <b style="">p</b> can be varied with
scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Number of heads and proportion of heads in <span
class="SpellE">Binomial</span> experiments</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BinomialTimelineExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BinomialTimelineExperiment</span>”
from the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment consists of performing <b><i
style="">n</i> Bernoulli trials</b>, each with probability of success <b
style=""><i style="">p</i></b>. The successes are recorded as red dots
on a timeline marked from 1 to n. The number of successes<b style=""> <i
style="">X</i></b> and the proportion of successes<b style=""> <i
style="">M</i></b> are recorded on each update. Either X or M can be
selected with the list box. The discrete probability density function
and moments of the selected variable are shown in blue in the
distribution graph and are recorded in the distribution table. On each
update, the empirical probability density function and moments of the
selected variable are shown in red in the distribution graph and are
recorded in the distribution table. The parameters n and p can be
varied with scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Number of heads and proportion of heads in <span
class="SpellE">Binomial</span> experiments </p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BirthdayExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BirthdayExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The birthday experiment is to <b>draw a
random sample of n balls with replacement from a population of m balls,
numbered from 1 to N</b>. We are interested in the random variable <b
style=""><i style="">V</i></b><u> </u>that gives the number of
distinct values in the sample, and the indicator variable <b style=""><i
style="">I</i></b> that indicates a duplicate sample Value. On each
update, the sample of balls is shown in the first graph; a ball that
duplicates a previously chosen ball is shown in red, and otherwise is
shown in green. The parameters m and n can be varied with scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Birthday Paradox as an experiment!</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BivariateGame</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_Games.html">here</a> and
select “<span class="SpellE">BivariateGame</span>” from the list.<span
style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_Games.html<span
style=""><o:p></o:p></span></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">Click in the graph to generate <span
class="SpellE">bivariate</span> data. The selected points are shown as
<b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
dots in the <span class="SpellE">scatter plot</span>, and the
coordinates are recorded in the first table. The second table gives the
<b style=""><i style="">μ</i></b> and <b style=""><i style="">σ</i></b>
of the x and y coordinates, and the correlation. In the graph, the
horizontal cross hair is centered at the mean of the x-data and extends
one standard deviation on either side. Similarly, the vertical cross
hair is centered at the mean of the y-data and extends one standard
deviation on either side. Finally, the least squares regression line is
shown in the <span class="SpellE">scatter plot.</span></p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Regression, correlation demo</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BivariateNormalExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BivariateNormalExperiment</span>” from
the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment generates a point (X, Y) from
a <span class="SpellE">bivariate</span> normal distribution with <b
style=""><i style="">μ</i></b> (0, 0). The point is shown graphically
as a <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
dot in the <span class="SpellE">scatter plot</span>, and the
coordinates are recorded on each update. The distribution regression
line is shown in blue in the <span class="SpellE">scatter plot</span>,
and the sample regression line is shown in <b style=""><span
style="color: rgb(255, 102, 0);">red</span></b>. The density function
and moments of X and of Y are shown in the distribution graphs, and the
moments are given in the distribution tables. The last table gives the
distribution and sample correlation. The distribution standard
deviations and correlations can be varied <span class="SpellE">within</span>
scroll bars.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Regression and <span class="SpellE">correlation</span>
demo where the data is randomly sampled from N(<b style="">μ,σ<sup>2</sup></b>)</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BivariateUniformExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BivariateUniformExperiment</span>”
from the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment
generates a point (X, Y) from a uniform distribution on a region of the
plane. Any of the following regions can be selected with the list box: </p>
<p style="text-align: center;" class="MsoNormal"><span
style="font-weight: bold;" class="GramE">the</span><span
style="font-weight: bold;"> square</span>: -6 < x < 6, -6 < y
<6; <br>
<span style="font-weight: bold;">the triangle</span>: -6 < y
< x < 6; and <br>
<span style="font-weight: bold;">the circle</span>: x<sup>2 </sup>+
y<sup>2 </sup> < 36.</p>
<p class="MsoNormal"><br>
The random point is shown has a <b style=""><span
style="color: rgb(255, 102, 0);">red</span></b> dot in the <span
class="SpellE">scatter plot</span>, and the coordinates are recorded
on each update. The <span class="SpellE">scatter plot</span> also
shows the distribution regression line in blue and the sample
regression line in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>.
The distribution and sample density and moments for X and for Y are
shown in the second and third graphs. The distribution and sample
moments are given in the second and third tables. The distribution and
sample correlation are given in the last table.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Regression and correlation demo where the
data is randomly sampled from Uniform Distribution </p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BuffonCoinExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BuffonCoinExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment consists of tossing a coin on
a floor with square tiles, and is shown graphically in the first
picture box. The center (X, Y) of the coin relative to the center of
the square is recorded on each update in the first table, and is shown
graphically as a <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
dot in the <span class="SpellE">scatter plot</span>. Variable <b
style=""><i style="">I </i></b><span class="GramE">indicates</span>
the event that the coin crosses a crack, and is recorded on each update
in the first table. The density of <b style=""><i style="">I</i></b>
is shown in the last graph in blue and is given in the second
table. When the experiment runs, the empirical density of <b style=""><i
style="">I</i></b> is shown in the last graph in <b style=""><span
style="color: rgb(255, 102, 0);">red</span></b> and is given in the
second table. The parameter of the process is the radius <b style=""><i
style="">r</i></b> of the coin, and can be varied with the scroll bar</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Calculus Based Probability</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>BuffonNeedleExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">BuffonNeedleExperiment</span>” from
the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal"><span class="SpellE">Buffon's</span> needle
experiment consists of dropping a needle on hardwood floor, with
floorboards of width 1. The experiment is shown graphically in the
first graph box. The angle <b style=""><i style="">X</i></b> of the
needle relative to the floorboard cracks and the distance <b style=""><i
style="">Y</i></b> from the center of the needle to the lower crack
are recorded in the first table on each update. Each point (X, Y) is
shown as a <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
dot in the <span class="SpellE">scatter plot</span>. The variable <b
style=""><i style="">I</i></b><u> </u>indicates the event that the
needle crosses a crack. The density of <b style=""><i style="">I</i></b>
is shown in blue in the distribution graph and is recorded in the
distribution table. On each update, the empirical density of <b
style=""><i style="">I</i></b> is shown in <b style=""><span
style="color: rgb(255, 102, 0);">red</span></b> in the distribution
graph and is also recorded in the distribution table. Finally, pi is
shown in blue in the last graph and is recorded in the last table, and
on each update, <span class="SpellE">Buffon's</span> estimate of pi is
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
in the last graph and is recorded in the last table.<span style="">
</span>The parameter is the needle length L, which can be varied
with a scroll-bar</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Calculus Based Probability </p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>CardExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">CardExperiment</span>” from the list.<span
style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal" style="margin-bottom: 12pt;">The experiment
consists of dealing n cards at random from a standard deck of 52 cards.
The denomination Yi and suit <span class="SpellE">Zi</span> of the <span
class="SpellE">i'th</span> card are recorded for <span class="SpellE">i</span>
= 1<span class="GramE">, ...,</span> n on each update. The
denominations are encoded as follows: </p>
<p style="text-align: center;" class="MsoNormal">1
(ace), 2-10, 11 (jack), 12 (queen), 13 (king).</p>
<p class="MsoNormal"><br>
The suits are encoded as follows: 0 (clubs), 1 (diamonds), 2 (hearts),
3 (spades). The parameter n can be varied with a scroll bar</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Probability</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>ChiSquareFitExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">ChiSquareFitExperiment</span>” from
the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment is to select a random sample
from a specified distribution and perform the <b style="">χ<sup>2</sup></b>
goodness of fit test to another specified distribution, at a specified
level of significance. The distributions are discrete distributions on
{1, 2, 3, 4, 5, 6}, and thus the experiment corresponds to rolling n
dice, each governed by the same distribution. The sampling and
test distributions can be specified by clicking on the die buttons
(these bring up the die probability dialog box. The density of
the true distribution is shown in blue in the first graph; the density
of the test distribution is shown in green. The significance level can
be selected from a list box and the sample size n can be varied with a
scroll bar. The test statistic <b style=""><i style="">V</i></b>
has (approximately) the <b style="">χ<sup>2</sup></b><sup> </sup>distribution
with 5 degrees of freedom. The density of <b style=""><i style="">V</i></b>
and the critical values are shown in <b style=""><span
style="color: blue;">blue</span></b> in the second graph. On each
update, the sample values are recorded in the first table and the
sample density is shown in red in the first graph. The value of the
test statistic <b style=""><i style="">V</i></b> is shown in red in
the second graph. Note that the null hypothesis is rejected if and only
if <b style=""><i style="">V</i></b> falls outside of the critical
values. Variable <b style=""><i style="">I</i></b> <span class="GramE">indicates</span>
the event that the null hypothesis is rejected. The empirical density
of <b style=""><i style="">I</i></b>, as the experiment runs, is shown
in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
in the last graph and is given in the last table. The values of <b
style=""><i style="">V</i></b> and <b style=""><i style="">I</i></b>
are recorded in the middle table on each update</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><o:p> </o:p></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>ChuckALuckExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">ChuckALuckExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">In the game of chuck-a-luck, a gambler
chooses an integer from 1 to 6 and then three fair dice are rolled. If
exactly k dice show the gambler's number, the payoff is k<span
class="GramE">:1</span>. The three dice are shown in the first picture
box on each update. Random variable W gives the gambler's net profit on
a $1 bet and is recorded in the first table on each update. The density
and moments of W are shown in <b style=""><span style="color: blue;">blue</span></b>
in the second picture box and are recorded in the second table. On each
update, the empirical density of <b style=""><i style="">W</i></b> is
shown in <b style=""><span style="color: rgb(255, 102, 0);">red</span></b>
in the second picture box and recorded in the second table</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><o:p> </o:p></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>CoinDieExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">CoinDieExperiment</span><b>:<o:p></o:p></b></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">” from the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The coin die experiment consists of first
tossing a coin, and then rolling a red die if the coin lands head or a
green die if the coin lands tails. The value of the coin (1 for heads
and 0 for tails) and the score on the die that is rolled are recorded
on each update. You can specify the die distribution of the dice by
clicking on the die probability buttons; these buttons bring up the die
probability dialog box. You can define your own distribution by typing
probabilities into the text fields of the dialog box, or you can click
on one of the buttons in the dialog box to specify one of the following
special distributions: fair, 1-6 flat, 2-5 flat, 3-4 flat, skewed left,
or skewed right. <span class="GramE">the</span> probability of heads p
for the coin can be varied with a scroll bar. The density and moments
of the die that is rolled are shown in the distribution graph and
distribution table</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal" style="margin-bottom: 12pt;">Conditional
Probability </p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>CoinSampleExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">CoinSampleExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment consists of tossing <b
style=""><i style="">n</i></b> <span class="GramE">coins,</span> each
with probability of heads p. Variable <span class="SpellE">Ij</span>
gives the outcome (1 for heads, 0 for tails) for coin <b style=""><i
style="">j</i></b>. The results are recorded on each update. The
parameters <b style=""><i style="">n</i></b> and <b style=""><i
style="">p</i></b> can <span class="SpellE">be varied</span> with
scroll bars</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Probability, law of large numbers</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;" valign="top">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>ConfidenceIntervalExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">ConfidenceIntervalExperiment</span>”
from the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">An experiment demonstrating the effects of <i>confidence
leve</i>l and <i>sample-size</i> on the <i>size </i>of the
constructed confidence interval. This experiment randomly samples from
a <span class="GramE"><i>N(</i></span><b style=""><i>μ</i></b><i>=0, <b
style="">σ<sup>2</sup></b>=1)</i> distribution and constructs a
confidence interval for the mean (<b style=""><i>μ</i></b>). The same
phenomena are observed when sampling from almost all symmetric <span
class="SpellE">unimodal</span> <span class="SpellE">distributions</span>.
Note how confidence interval widens as the confidence level increases.
This is counterbalanced by the sample-size increase. Also, see the
effect of the confidence level, <i>100(1-<b style="">α</b><span
class="GramE">)%</span></i>, on the frequency of intervals missing the
estimated parameter (<b style=""><i>μ</i></b><i>=0</i>, in this case).</p>
</td>
<td
style="padding: 1.5pt; text-align: center; vertical-align: middle;">
<p class="MsoNormal">Confidence intervals, margins of error.</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>CouponCollectorExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">CouponCollectorExperiment</span>” from
the list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The coupon collector experiment consists of
sampling with replacement from the population {1, 2<span class="GramE">,
...,</span> m} until <b style=""><i style="">k</i></b> distinct values
are obtained. The first graph gives the counts for each population
value that occurred in the sample. Random variable <b style=""><i
style="">W</i></b> gives the sample size and is recorded in the first
table on each update. The density and moments of <b style=""><i
style="">W</i></b> are shown in <b style=""><span style="color: blue;">blue</span></b>
in the second graph and are recorded in the second table. On each
update, the empirical density and moments of W are shown in red in the
second graph and are recorded in the second table. The parameters <b
style=""><i style="">m</i></b> and <b style=""><i style="">k</i></b>
can be varied with scroll bars</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><o:p> </o:p></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>CrapsExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">CrapsExperiment</span>” from the list.<span
style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">In the game of craps, the shooter rolls a
pair of fair die. The rules are as follows: If the shooter rolls a sum
of 7 or 11 on the first roll, she wins. If the shooter rolls a sum of
2, 3, or 12 on the first roll, she loses. If the shooter rolls a sum of
4, 5, 6, 8, 9, or 10, this number becomes the shooter's point. The
shooter continues to roll the dice until the sum is either the point
(in which case she wins) or 7 (in which case she loses). Any of the
following bets can be selected: Pass: this is the bet that the shooter
will win, and pays 1:1. Don't Pass: this is the bet that the shooter
will lose, except that an initial roll of 12 is excluded (that is, the
shooter loses, but <span class="GramE">the don't</span> pass bettor
neither wins nor loses). The bet pays 1:1. Field: this is a bet on a
single throw. <br>
<br>
It pays 1:1 if 3, 4, 9, 10, or 11 is thrown, 2:1 if 2 or 12 is thrown,
and loses otherwise. Craps: this is a bet that 2, 3, or 12 will come up
on a single throw, and pays 7:1. Craps 2: this is a bet that 2 will
come up on a single throw, and pays 30:1. Craps 3: this is a bet that 3
will come up on a single throw, and pays 15:1. Craps 12: this is a bet
that 12 will come up on a single throw, and pays 30:1. Seven: this is a
bet that 7 will come up on a single throw, and pays 4:1. Eleven: this
is a bet that 11 will come up on a single throw, and pays 15:1. Big 6.
This is a bet that 6 will be thrown before 7, and pays 1:1. Big 8: this
is a bet that 8 will be thrown before 7, and pays 1:1. <span
class="SpellE">Hardway</span> 4: this is a bet that (2, 2) will be
thrown before 7 or any other 4, and pays 7:1. <span class="SpellE">Hardway</span>
6. <span class="GramE">this</span> is a bet that (3, 3) will be thrown
before 7 or any other 6, and pays 9:1. <span class="SpellE">Hardway</span>
8: this is a bet that (4, 4) will be thrown before 7 or any other 8,
and pays 9:1. <span class="SpellE">Hardway</span> 10: this is a bet
that (5, 5) will be thrown before 7 or any other 10, and pays 7:1</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Probability</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>DiceExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">DiceExperiment</span>” from the list.<span
style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment consists of rolling <b
style=""><i style="">n</i></b> dice, each governed by the same
probability distribution. You can specify the die distribution by
clicking on the die probability button; <span class="GramE">this
button bring</span> up the die probability dialog box. You can define
your own distribution by typing probabilities into the text fields of
the dialog box, or you can click on one of the buttons in the dialog
box to specify one of the following special distributions<span
class="GramE">:</span><br>
<br>
</p>
fair, 1-6 flat, 2-5 flat, 3-4
flat, skewed left, or skewed right. <br>
<p class="MsoNormal"> <br>
The following random variables are recorded on each update: the sum of
the scores <b style=""><i style="">Y</i></b>, the <span class="GramE">average
score</span> <b style=""><i style="">M</i></b>, the minimum score <b
style=""><i style="">U</i></b> the maximum score <b style=""><i
style="">V</i></b>, the number of aces (1's) <b style=""><i style="">Z</i></b>.
Any one of these variables can be selected with a list box. The density
and moments of the selected variable are shown in <b style=""><span
style="color: blue;">blue</span></b> in the distribution graph and are
recorded in the distribution table. When the simulation runs, the
empirical density and moments are shown in <b style=""><span
style="color: rgb(255, 102, 0);">red</span></b> in the distribution
graph and are recorded in the distribution table. The parameter <b
style=""><i style="">n</i></b> can be varied with a scroll bar.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal">Discrete variables</p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>DiceSampleExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">DiceSampleExperiment</span>” from the
list.<span style=""> </span><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: center;" align="center"><b><o:p> </o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center">SOCR_experiments.html</p>
<p class="MsoNormal" style="text-align: center;" align="center"><o:p> </o:p></p>
</td>
<td
style="padding: 1.5pt; vertical-align: middle; text-align: justify;">
<p class="MsoNormal">The experiment consists of rolling <b
style=""><i style="">n</i></b> dice, each governed by the same
probability distribution. You can specify the die distribution by
clicking on the die probability button; this button brings up the die
probability dialog box. You can define your own distribution by typing
probabilities into the text fields of the dialog box, or you can click
on one of the buttons in the dialog box to specify one of the following
special distributions: fair, 1-6 flat, 2-5 flat, 3-4 flat, skewed left,
or skewed right. The number of dice can be varied with a scroll bar.
The scores of each die are recorded in the table.</p>
</td>
<td
style="padding: 1.5pt; width: 25%; text-align: center; vertical-align: middle;"
width="25%">
<p class="MsoNormal"><o:p> </o:p></p>
</td>
</tr>
<tr style="">
<td style="padding: 1.5pt; width: 25%;">
<p class="MsoNormal" style="text-align: center;" align="center"><span
class="SpellE"><b>DieCoinExperiment</b></span><b>:<o:p></o:p></b></p>
<p class="MsoNormal" style="text-align: center;" align="center"><span
style="">To view this experiment, click <a
href="http://socr.stat.ucla.edu/htmls/SOCR_experiments.html">here</a>
and select “<span class="SpellE">DieCoinExperiment</span>” from the