This page contains course notes and homework assignments with solutions for a mathematical statistics class. The course covers statistical inference, probability, and estimation principles.
This file applies the Cramer-Rao inequality to a binomial random variable to prove that the usual estimator of p is a minimum variance unbiased estimator.
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.
