Limit Theorems

• Sample Means

This site gives an explanation of, a definition for and an example of sample means. Topics include mean, variance, distribution, and the Central Limit Theorem.
• Games of Chance

This online, interactive lesson on games of chance provides examples, exercises, and applets which include Poker, Poker dice, Chuck-a-Luck, Craps, Roulette, The Monty Hall Problem, lotteries, and Red and Black.
• Central Limit Theorem

Illustrates the central limit theorem by allowing the user to increase the number of samples in increments of 100, 1000, or 10000.

• Analysis Tool: Basic Multiple Regression

This page will perform basic multiple regression analysis for the case where there are several independent predictor variables, X1, X2, etc., and one dependent or criterion variable, Y. Requires import of data from a spreadsheet.

• Law of Large Numbers (Chapter 8)

Part of an online statistics textbook. Topics include: (1) Law of Large Numbers for Discrete Random Variables, (2) Chebyshev Inequality, (3) Law of Averages, (4) Law of Large Numbers for Continuous Random Variables, (5) Monte Carlo Method. There are several examples and exercises that accompany the material.
• Significance Level

This resource briefly explains what a significance level is and how they are used in hypothesis testing. It also includes other links related to significance level such as "Type I error" and "significance test".
• Central Limit Theorem JAVA Applet

This applet simulates rolling dice to illustrate the central limit theorem. The user can choose between 1, 2, 6, or 9 dice to roll 1, 5, 20, or 100 times. The distribution is graphically displayed. This applet needs to be resized for optimal viewing.

• Chebychev's Estimate

For n = 50 to 400, in steps of size 5, this program computes and displays (1) the exact probability P(|A_n - p| >= epsilon), where A_n is the average outcome of n Bernoulli trials with probability p of success, and (2) the Chebyshev estimate p(1-p)/(n(epsilon^2)) for this probability. You can specify p and epsilon.
• Analysis Tool: Matrix of Intercorrelations (Data-import format)

This page will calculate the intercorrelations (r) for any number of variables (V1, V2, V3, etc.) and for any number of observations per variable.

• The Central Limit Theorem Applets

The applets in this section of Statistical Java allow you to see how the Central Limit Theorem works. The main page gives the characteristics of five non-normal distributions (Bernoulli, Poisson, Exponential, U-shaped, and Uniform). Users then select one of the distributions and change the sample size to see how the distribution of the sample mean approaches normality. Users can also change the number of samples. To select between the different applets you can click on Statistical Theory, the Central Limit Theorem and then the Main Page. At the bottom of this page you can make your applet selection. This page was formerly located at http://www.stat.vt.edu/~sundar/java/applets/