Dice Experiment

Description and Use

The experiment consists of rolling n dice, each governed by the same probability distribution. You can specify the die distribution by clicking on the die probability button; this button 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: each face has probability 1/6
1-6 flat: faces 1 and 6 have probability 1/4 each; faces 2, 3, 4, and 5 have probability 1/8 each.
2-5 flat: faces 2 and 5 have probability 1/4 each; faces 1, 3, 4, and 6 have probability 1/8 each.
3-4 flat: faces 3 and 4 have probability 1/4 each; faces 1, 2, 5, and 6 have probability 1/8 each.
skewed left: face i has probability i / 21 for i = 1, 2, 3, 4, 5, 6.
skewed right: face i has probability (7 - i) / 21 for i = 1, 2, 3, 4, 5, 6.

The following random variables are recorded on each update:

The sum of the scores Y.
The average score M.
The minimum score U.
The maximum score V.
The number of aces (1's) Z.

Any one of these variables can be selected with a list box. The density and moments of the selected variable are shown in blue in the distribution graph and are recorded in the distribution table. When the simulation runs, the empirical density and moments are shown in red in the distribution graph and are recorded in the distribution table. The parameter n can be varied with a scroll bar.

This experiment uses the die as a metaphor for a random variable taking a finite set of values, and involves a number of standard transformations. Thus, the experiment illustrates the central limit theorem, the law of large numbers, the distribution of the sample mean, and the distribution of the extreme order statistics. For a more detailed mathematical analysis, see

Instructions for Downloading and Installing

Click on the link below to download the Java archive file:

DiceExperiment.jar (78 KB)

To add the applet to your web page, insert the following in the html file, at the point where you want the applet to appear:

<applet code="edu.uah.math.experiments.DiceExperiment.class" archive="DiceExperiment.jar" width="500" height="400"></applet>

The jar file and the html file must be in the same folder.

This width and height dimensions are simply suggestions and can be varied. Generally, components such as graphs and tables expand and contract proportionally, while components such as buttons, scrollbars, dice, and coins are fixed in size.

Metadata

Type

Java Applet

Keywords

probability
statistics
dice
random variable
law of large numbers
central limit theorem

Version

August, 2003

Browser Requirements

Support for the Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate plug-in.

Authors

Kyle Siegrist
Dawn Duehring

Copyright

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.

Related Resources

If you are interested in the Java source code or the Java documentation and object model for this applet, please visit DiceExperiment in the Object section of the Library.