Probability and Statistics for Computer Scientists, 2nd Edition

Chapter 3

Discrete Random Variables and Their Distributions

This chapter introduces the concept of a random variable and studies discrete distributions in detail. Continuous distributions are discussed in Chapter 4.

3.1 Distribution of a random variable

3.1.1 Main concepts

Definition 3.1

A random variable is a function of an outcome,

$X=f(\omega ).$

In other words, it is a quantity that depends on chance.

The domain of a random variable is the sample space Ω. Its range can be the set of all real numbers $ℝ$, or only the positive numbers (0, +∞), or the integers $\mathbb{Z}$, or the interval (0, 1), etc., depending on what possible values the random variable can potentially take.

Once an experiment is completed, and the outcome ω is known, the value of random variable ...