Probability

  • This site contains data sets to help teach a Chance course and help students understand issues that may not be found in a standard statistics text. Topics covered include: mean, median, random walks, regression, correlation, and more.
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  • 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.

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  • The Marble Game is a "concept model" demonstrating how a binomial distribution evolves from the occurence of a large number of dichotomous events. The more events (marble bounces) that occur, the smoother the distribution becomes.
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  • This is an exercise in interpreting data that is generated by a phenomenon that causes the data to become biased. You are presented with the end product of this series of events. The craters occur in size classes that are color-coded. After generating the series of impacts, it becomes your assigned task to figure out how many impact craters correspond to each of the size class categories.
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  • This website contains more real analysis, general topology and measure theory than actual probability. It is more about the foundations of probability theory, than probability itself. In particular, it is a very suitable resource for anyone wishing to study the Lebesgue integral. These tutorials are designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved Theorems, as well as clear Definitions are spelt out for future reference. These tutorials do not contain any formal proof: instead, they will offer you the means of proving everything yourself. However, for those who need more help, Solutions to exercises are provided, and can be downloaded.
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  • This site contains lessons which include steps, examples, and a calculator, on standard deviation, Pearson's r, t-test, one-way ANOVA, and Tukey's Post Hoc Test.
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  • This pdf file gives definitions for average, standard deviation, and relative standard deviation, and works through a short problem as an example.
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  • This page introduces various measures of central tendency and spread with an example on leaf size. Two descriptive statistics calculators are provided which compute mean, median, minimum, maximum, 1st & 3rd quartiles, standard deviation, and the 95% confidence interval for the mean and tests for normality. Users type in individual data points or copy and paste the entire data set. Key Words: Five Number Summary; Mode; Interquartile Range; Variance; Range; Normal Distribution.
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  • This online, interactive lesson on random samples provides examples, exercises, and applets concerning sample mean, law of large numbers, sample variance, partial sums, central limit theorem, special properties of normal samples, order statistics, and sample covariance and correlation.
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  • This online, interactive lesson on geometric models provides examples, exercises, and applets which include Buffon's Problems, Bertrand's Paradox, and Random Triangles.

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