Calculus required

  • This online, interactive lesson on point estimation provides examples, exercises, and applets concerning estimators, method of moments, maximum likelihood, Bayes estimators, best unbiased estimators, and sufficient, complete and ancillary statistics.
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  • 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.

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  • 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.

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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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  • 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.

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

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  • 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.

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  • This online, interactive lesson on Markov chains provides examples, exercises, and applets that cover recurrence, transience, periodicity, time reversal, as well as invariant and limiting distributions.
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  • This set of pages describes software the author wrote to implement bootstrap and resampling procedures. It also contains an introduction to resampling and the bootstrap; and examples applying these procedures to the mean, the median, correlation between two groups, and analysis of variance.
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  • This journal article is a summary of resampling methods such as the jackknife, bootstrap, and permutation tests. It summarizes the tests, describes various software to perform the tests, and has a list of references.
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