# Simulation

• ### Descriptive Statistics Calculator

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.
• ### Set Estimation

This online, interactive lesson on set estimation provides examples, exercises, and applets concerning estimation of the normal model, estimation in the Bernoulli Model, estimation in the two-sample normal model, and Bayesian set estimation.

• ### Hypothesis Testing

This online, interactive lesson on hypothesis testing provides examples, exercises, and applets which includes tests in the normal model, Bernoulli Model, and two-sample normal model as well as likelihood ratio and goodness of fit tests.

• ### Geometric Models

This online, interactive lesson on geometric models provides examples, exercises, and applets which include Buffon's Problems, Bertrand's Paradox, and Random Triangles.

• ### Probability Spaces

This online, interactive lesson on probability spaces provides examples, exercises, and applets that cover conditional probability, independence, and several modes of convergence that are appropriate for random variables. This section also covers probability space, the paradigm of a random experiment and its mathematical model as well as sample spaces, events, random variables, and probability measures.

• ### Markov Chains

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.
• ### Resampling Statistics: Randomization and the Bootstrap

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.
• ### Resampling methods: Concepts, Applications, and Justification

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.
• ### BGIM : Maximum Likelihood Estimation Primer

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