CHAPTER 4 - Discrete Distributions

Abstract

This chapter provides an overview of discrete distributions. A univariate distribution function is the distribution function of a single random variable. A sequence of n Bernoulli trials is a game consisting of n trials, which satisfy the three requirements: (i) one of the two possible incompatible events, denoted by S and F, occurs as the outcome of each trial, (ii) the outcome of each trial is independent of the outcomes of the other trials, and (iii) the probability of S occurring at a trial does not change from trial to trial. Hypergeometric distribution is obtained through sampling without replacement. The Poisson distribution can be obtained as an approximation to the binomial distribution when the probability of success is small and Bernoulli trials are large. The chapter discusses two important joint discrete density functions: the multivariate hypergeometric distribution and the multinomial distribution. Conditional discrete densities are nothing other than the conditional probabilities of events. The multinomial distribution can be derived using the notion of conditional density.