Some Probability Distributions and Their Uses

In the distributions chapter we study the following distributions: Bernoulli Trials, binomial, poisson, exponential, Cauchy, normal, lognormal, beta, gamma, and composit. For each we give the density and cumulative distribution functions and calculate their mean and variance. At the same time we introduce several sampling techniques: cdf inversion, simulation, transformation, and rejection. Important Theorems presented with applications are the Central Limit Theorem and Gibrat’s Theorem. Useful applications stemming directly from studying the distributions are: discrete event simulation, batching for analyzing Monte Carlo results, and calculating error bounds by invoking the Central Limit Theorem and the student-t distribution.