Curriculum

  • 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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  • This set of pages is an introduction to Maximum Likelihood Estimation. It discusses the likelihood and log-likelihood functions and the process of optimizing.
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  • This journal article gives examples of erroneous beliefs about probability. It specifically examines the belief that a random sample must be representative of the true population.
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  • This journal article describes a set of experiments in which different methods of teaching Bayes' Theorem were compared to each other. The frequency representation of the rule was found to be easier to learn than the probability representation.
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  • This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.
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