Chapter 5 - Probability Distributions of Discrete Variables: For this chapter the reader should have a solid understanding of sections 2.1, 2.2, 3.1, and 3.2

Abstract

This chapter discusses discrete random variables and their probability and distribution functions. It briefly describes the idea of mathematical expectation or the mean of a probability distribution and the concept of the variance of a probability distribution, and explains the two important discrete probability distributions: the Binomial Distribution and the Poisson Distribution. Probability Functions and Distribution Functions are also discussed. The functional relationship between the cumulative probability and the upper limit, x, is called the cumulative distribution function or the probability distribution function. The chapter describes the expectations and variance. The mathematical expectation or the expected value of a random variable is an arithmetic mean that we can expect to closely approximate the mean result from a very long series of trials, if a particular probability function is followed. In the great majority of problems given, a tree diagram will be very desirable. Binomial distribution applies in some cases to repeated trials where there are only two possible outcomes. The probability of each outcome can be calculated using the multiplication rule, perhaps with a tree diagram, but it is usually much faster and more convenient to use a general formula. The requirements for using the binomial distribution are also mentioned.