Probability with R, 2nd Edition

9Introduction to Discrete Distributions

In this chapter, we introduce the concepts of discrete random variables and expectation and go on to develop basic techniques for examining them by simulation in R. Along the way, we introduce the Bernoulli and uniform discrete distributions. We end the chapter with an introduction to discrete bivariate distributions.

9.1 Discrete Random Variables

A random variable is a rule that assigns a numerical value to each possible outcome of an experiment, that is, a mapping from the sample space to the number line. It is said to be discrete if its values assume integer points on the number line, that is, the outcomes are finite or countably infinite. Discrete random variables are in effect numerical representations of discrete sample spaces.

Definition 9.1 Discrete distributions

The set of all possible values of a discrete variable, together with their associated probabilities, is called a discrete probability distribution.

Let us look at some of the examples considered in Chapter 4 and show how to obtain their probability distributions.

Example 9.1 Toss a fair coin

Let = 1 if a head occurs, and = 0 if a tail occurs. Since the coin is fair, ...