Resource Library

This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.

This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.

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.

This set of pages is an introduction to Maximum Likelihood Estimation. It discusses the likelihood and log-likelihood functions and the process of optimizing.

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.

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.

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.

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.

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.

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.