ABSTRACT
In this chapter we study the fundamental concept of the distribution of a variable X defined on a sample space. A variable defined on a sample space is called a random variable. It is analogous to the concept of a variable defined on a population S studied earlier in Chapter 1. There are other analogies as well: The analogue of the empirical distribution function is called the distribution function of X , and the analogues of the sample mean and sample variance are called the expected value and variance of X, respectively. Random variables are classified as discrete or continuous; the major difference between these two types is in the level and sophistication of the mathematical tools that one uses to study them. In this chapter we study only discrete random variables; the concept of a continuous random variable, which requires calculus in an essential way, will be treated in Chapter 4.
