Essentials of Mathematical Statistics

CHAPTER 2

Discrete Random Variables

Chapter Objectives

• Define random variables

• Define discrete random variables and the probability mass function

• Introduce the hypergometric, binomial, and Poisson distributions

• Define the mean, the variance, and functions of a random variable

• Introduce the moment-generating function

2.1   Introduction

Outcomes of random experiments take many different forms. They could be colors, such as when we select a cube from a bag and note its color. They could be yes-or-no answers to questions, such as when we ask people if they support a candidate running for office. Or they could be sequences of results from a set of trials, such as when we flip a coin three times.

It is often convenient to associate a number ...