• ### Belief in the Law of Small Numbers

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.
• ### Sufficient Statistics

This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.
• ### Analysis Tool: Empirical Distributions

This applet plots the survival function (1-F(t)) of the exponential distribution against the empirical survival function. The empirical survival function is one minus the empirical distribution function.

• ### Analysis Tool: Empirical Cumulative Distribution

This applet allows the user to enter data, then returns the values of empirical cumulative distribution function by sorting the data and reporting the height of the curve at each point. It does not show the graph.

• ### The Cramer-Rao Lower Bound

This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.
• ### Cramer-Rao Lower Bound: an Example

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.
• ### Statistical Inference

This page contains course notes and homework assignments with solutions for a mathematical statistics class. The course covers statistical inference, probability, and estimation principles.
• ### Properties of an Estimator

These slides address point estimation including unbiasedness and efficiency and the Cramer-Rao lower bound.
• ### Theoretical Underpinnings of the Bootstrap

This page discusses the theory behind the bootstrap. It discusses the empirical distribution function as an approximation of the distribution function. It also introduces the parametric bootstrap.
• ### Advanced Statistics - Biology 603 - Lectures

This site provides links to lecture outlines for an upper-level statistics class. Topics include hypothesis testing, ANOVA and regression.