# Limit Theorems

• ### Random Samples

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.
• ### 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.
• ### 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.

• ### 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.
• ### Exploratory Data Analysis Case Studies (Engineering Statistics Handbook)

This part of the NIST Engineering Statistics Handbook contains case studies for Exploratory Data Analysis. Some of the topics include normal and uniform random numbers, reliability using airplane glass failure times, and analysis of primary factors using ceramic strength.
• ### Electronic Statistics Textbook

This Electronic Statistics Textbook offers training in the understanding and application of statistics ... and covers a wide variety of applications, including laboratory research (biomedical, agricultural, etc.), business statistics and forecasting, social science statistics and survey research, data mining, engineering and quality control applications, and many others. Quoted from the index page of the text.
• ### Teaching with, and preparing guided notes for your lecture

A useful site for instructors to learn how to create and incorporate guided notes into their classroom.