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 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.
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 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.
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 page introduces various measures of central tendency and spread with an example on leaf size. Two descriptive statistics calculators are provided which compute mean, median, minimum, maximum, 1st & 3rd quartiles, standard deviation, and the 95% confidence interval for the mean and tests for normality. Users type in individual data points or copy and paste the entire data set. Key Words: Five Number Summary; Mode; Interquartile Range; Variance; Range; Normal Distribution.
