Bernoulli Trials and Discrete Distributions

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Abstract
This tutorial paper defines a process in terms of Bernoulli random variables and develops a number of discrete distributions based on this formulation. The distributions are the binomial, geometric, hypergeometric, negative binomial, beta-binomial, multinomial, and Poisson. Also included is the application of the Bernoulli to run- and segmentation-type problems. For each of the models covered a description is given of the type of process it applies to and some of its elementary features such as its probability function, distribution function (including sources of tables, where appropriate), parameter estimates, formulas for the confidence interval, and relationships with other distributions. Several examples of how each model is used are also presented. References are given where more detailed information may be obtained.