Curriculum

  • 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 Java applet tutorial prompts the user to input the components of a hypothesis test for the mean. Hints are provided whenever the user enters an incorrect value. Once the steps are completed and the user has chosen the correct conclusion for accepting or rejecting the null hypothesis, a statement summarizing the conclusion is displayed. The applet is supported by an explanation of the steps in hypothesis testing and a description of one-tailed and two-tailed tests.
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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 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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