### Introduction

If an engineer is responsible for the quality of, say, copper wire for use in domestic wiring systems, he or she might be interested in knowing both the number of faults in a given length of wire and also the distances between such faults. While the number of faults may be analysed by using the Poisson distribution, the distances between faults along the wire may be shown to give rise to the exponential distribution defined and used in this Section.

#### Prerequisites

• understand the concepts of probability
• be familiar with the concepts of expectation and variance
• be familiar with the concepts of continuous distributions, in particular the Poisson distribution.

#### Learning Outcomes

• understand what is meant by the term exponential distribution
• calculate the mean and variance of an exponential distribution
• use the exponential distribution to solve simple practical problems