# Resource Library

#### Statistical Topic

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• ### Probability Spaces

This online, interactive lesson on probability spaces provides examples, exercises, and applets that cover conditional probability, independence, and several modes of convergence that are appropriate for random variables. This section also covers probability space, the paradigm of a random experiment and its mathematical model as well as sample spaces, events, random variables, and probability measures.

• ### Set Estimation

This online, interactive lesson on set estimation provides examples, exercises, and applets concerning estimation of the normal model, estimation in the Bernoulli Model, estimation in the two-sample normal model, and Bayesian set estimation.

• ### Hypothesis Testing

This online, interactive lesson on hypothesis testing provides examples, exercises, and applets which includes tests in the normal model, Bernoulli Model, and two-sample normal model as well as likelihood ratio and goodness of fit tests.

• ### Geometric Models

This online, interactive lesson on geometric models provides examples, exercises, and applets which include Buffon's Problems, Bertrand's Paradox, and Random Triangles.

• ### Analysis Tool: Statistics Online Computational Resources (SOCR)

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.

• ### Analysis Tool: Empirical Cumulative Distribution

This applet allows the user to enter data, then returns the values of empirical cumulative distribution function by sorting the data and reporting the height of the curve at each point. It does not show the graph.

• ### Analysis Tool: Empirical Distributions

This applet plots the survival function (1-F(t)) of the exponential distribution against the empirical survival function. The empirical survival function is one minus the empirical distribution function.

• ### Free Statistics Software

This site is a collection of Web-enabled scientific services & applications including Equation Plotter Software, Scientific Forecasting Software, Multiple Regression Software, Descriptive Statistics Software, Statistical Hypothesis Testing Software, Sample Size Software, and XML-RPC PHP client.

• ### Renewal Processes Apps

This online, interactive lesson on the renewal processes provides examples, exercises, and applets which include renewal equations and renewal limit theorems.

• ### Probability, Mathematical Statistics, and Stochastic Processes

This online, interactive lesson on finite sampling models provides examples, exercises, and applets that include hypergeometric distribution, multivariate hypergeometric distribution, order statistics, the matching problem, the birthday problem, and the coupon collector problem.