### Introduction

It is often possible to model real systems by using the same or similar random experiments and their associated random variables. Numerical random variables may be classified in two broad but distinct categories called discrete random variables and continuous random variables. Often, discrete random variables are associated with counting while continuous random variables are associated with measuring. In
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HELM booklet
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42. you will meet contingency tables and deal with non-numerical random variables. Generally speaking, discrete random variables can take values which are separate and can be listed. Strictly speaking, the real situation is a little more complex but it is sufficient for our purposes to equate the word discrete with a finite list. In contrast, continuous random variables can take values anywhere within a specified range. This Section will familiarize you with the idea of a discrete random variable and the associated probability distributions. The Workbook makes no attempt to cover the whole of this large and important branch of statistics but concentrates on the discrete distributions most commonly met in engineering. These are the binomial, Poisson and hypergeometric distributions.

#### Prerequisites

- understand the concepts of probability

#### Learning Outcomes

- explain what is meant by the term discrete random variable
- explain what is meant by the term discrete probability distribution
- use some of the discrete probability distributions which are important to engineers

#### Contents

1 Discrete probability distributions1.1 Permutations and Combinations

1.2 Factorials

1.3 Permutations

1.4 Combinations

2 Random variables

2.1 Discrete random variables and probability distributions

3 Mean and variance of a discrete probability distribution