This chapter of the HyperStat Online Textbook discusses in detail sampling distributions of various statistics (mean, median, proportions, correlation, etc.), differences between such statistics, the Central Limit Theorem, and standard error, giving formulas, examples, and exercises.
This applet simulates rolling dice and displays the outcomes in a histogram. Students can choose to roll 1, 2, 6, or 9 dice either 1, 10, 20, or 100 times. The outcome studied is the sum of the dice and a red line is drawn on the histogram to show expected number of occurences of each outcome.
This is a "Building Block" for the Buffon Needle problem. The source code and compile code are included as well as separate files for each. Users able to test the applet to determine if it meets their needs.
This page supports an in-class exercise that highlights several key Bayesian concepts. The scenario is as follows: a large paper bag contains pieces of candy with wrappings of different color, and we are interested in learning about the unknown proportion of yellow-wrapped pieces of candy. After completing the exercises, we will be familiar with the following concepts and ideas: probability distributions can quantify degree of belief, prior distribution, posterior distribution, sequential updating, conjugacy, Cromwell’s Rule (http://en.wikipedia.org/wiki/Cromwell's_rule), the data overwhelm the prior, Bayes factors, Savage-Dickey density ratio, sensitivity analysis, coherence.
This applet shades the graph and computes the probability of X, when X is between two parameters x1 and x2. The user inputs the mean, standard deviation, x1 and x2. This applet should be resized for optimal viewing.
This page of Statistical Java describes 11 different probability distributions including the Binomial, Poisson, Negative Binomial, Geometric, T, Chi-squared, Gamma, Weibull, Log-Normal, Beta, and F. Each distribution has its own applet in which users can manipulate the parameters to see how the distribution changes. The parameters are described on the main page as well as situations that would use each distribution. The equations of the distributions are not given. To select between the different applets you can click on Statistical Theory, Probability Distributions 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/
This activity allows the user to simulate pulling red and green balls out of three boxes. The boxes are pre-arranged so that there are two red balls in one box, two green balls in another, and one green and one red ball in the third. The user can shuffle the order of the boxes and the order of the balls in the boxes. To run in single trial mode, click on one of the box to see if the first ball is green. If it is, click on the box again to see if the second ball is green also. A count will be kept of the results. To run in multiple trial mode, enter the number of trials desired in the box and click on the run multiple trials button. This activity would work well in groups of two to three for about twenty minutes if you use the exploration questions provided and ten minutes otherwise.
This activity allows the user to experiment with expected values by changing probabilities and payoffs for two people buying stocks, repeating the experiment up to 100 times. There are links to discussion topics and activities related to the applet.
This site gives an explanation, a definition and an example of correlation. Topics include correlation coefficient and rŒ_.
This applets on this site include: interactive graphs of many distribution models; a collection of computer generated games; a collection of data modeling aids including curve fitting, wavelets, matrix manipulations, etc.; p-values, quantiles & tail-probabilities calculations; virtual online probability experiments and demonstrations; and a large collection of statistical techniques for online data analysis, visualization, and integration.