When the variables of a scientific model are related through a chance mechanism, we call it a statistical model. This book covers statistical models for discrete variables. Its main focus is on the methods for analysis of discrete variable statistical models called exact conditional methods. This chapter prepares the groundwork. This includes introducing a unified framework for representing common discrete probability distributions, defining key concepts and describing the properties of these distributions. The specific aims here are:

• To state the properties of the binomial, Poisson, negative binomial, hypergeometric and related distributions.