# Conditional Probability

• ### Song: Use a t

Song describes conditions for using the t distribution and mentions its inventor William Gosset (and his pseudonym, Student). May be sung to the tune of "Let it Be" (McCartney/Beatles). Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.
• ### Time-Axis Fallacy and Bayes Theorem

This site provides an outline of an activity for introducing Bayes' Theorem and conditional probability.
• ### Analysis Tool: The BUGS Project

The BUGS (Bayesian inference Using Gibbs Sampling) project is concerned with flexible software for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. This site is primarily concerned with the stand-alone WinBUGS 1.4.1 package, which has a graphical user interface and on-line monitoring and convergence diagnostics. This program can be downloaded for free from the site.

• ### Conditional Probability and Probability of Simultaneous Events

This site provides applets, lessons, and objectives for learning about conditional probability. The applet activity introduces multiple-outcomes events and computing probabilities.
• ### A Tutorial on Mathematical Modeling

This general, introductory tutorial on mathematical modeling (in pdf format) is intended to provide an introduction to the correct analysis of data. It addresses, in an elementary way, those ideas that are important to the effort of distinguishing information from error. This distinction constitutes the central theme of the material described herein. Both deterministic modeling (univariate regression) as well as the (stochastic) modeling of random variables are considered, with emphasis on the latter. No attempt is made to cover every topic of relevance. Instead, attention is focussed on elucidating and illustrating core concepts as they apply to empirical data.

• ### Teaching Bayesian Reasoning in Less Than Two Hours

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.
• ### Conditional Probability

This site gives an explanation, a definition and an example of conditional probability. Topics include the probabilities of intersections of events and Bayes' formula.
• ### Two-Way Tables and the Chi-Square Test

This site gives an explanation, a definition and an example of two-way tables and the chi-square test. Topics include: categorical data analysis for two variables, and tests of association.
• ### Probability

Here one finds a collection of applets and famous problems in probability (as well as other areas of mathematics such as calculus and geometry). Some of the topics/problems include: Bertrand's Paradox, Birthday Coincidence, Buffon's Needle (Noodle), Lewis Carroll's Problem, Monty Hall Dilemma, Parrondo Paradox, and Three pancakes problem.

• ### t-Distribution Generator

Generate a graphic and numerical display of the properties of the t-distribution for values of df between 4 and 200, inclusive.