Principles of Managerial Statistics and Data Science

6Discrete Random Variables

6.1 Introduction

Up until now, to obtain probabilities for an event, we had to consider all the possibilities in the sample space and the ways that the event can occur. But, in many real‐life situations, it is very difficult to do this in a practical way. In addition, usually our interest is in the characteristics of the data collection procedure that can be obtained based on some sort of counting or some measure. A random variable is a function of the outcomes of a data collection procedure. It turns outcomes of the data collection procedures into a number. If this number is representative of the count of something, then it is a discrete random variable. If this number is representative of the measure of something (e.g. the length, weight, duration, etc.), then it is a continuous random variable.

In this chapter, we will work with probabilities, expected value, and variance of discrete random variables.

Random Variables and Their Nomenclature

In algebra courses, variables are used to generalize situations. In statistics, random variables are slightly different to the variables used in algebra. Since random variables are a function of the data collection procedure, which has random outcomes, random variables involve uncertainty as well, and hence we must characterize this uncertainty. On the other hand, variables in algebra do not involve any randomness. Capitalized letters such as , or are used to define a random variable, while specific values ...