### Introduction

It is often possible to model real systems by using the same or similar random experiments and their associated random variables. Random variables may be classified in two distinct categories called discrete random variables and continuous random variables. Discrete random variables can take values which are discrete and which can be written in the form of a list. In contrast, continuous random variables can take values anywhere within a specified range. This Section will familiarize you with continuous random variables and their associated probability distributions. This Workbook makes no attempt to cover the whole of this large and important branch of statistics. The most commonly met continuous random variables in engineering are the Uniform, Exponential, Normal and Weibull distributions. The Uniform and Exponential distributions are introduced in Sections 38.2 and 38.3 while the Normal distribution and the Weibull distribution are covered in
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39 and
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46 respectively.

#### Prerequisites

- understand the concepts of probability
- be familiar with the concepts of expectation and variance

#### Learning Outcomes

- explain what is meant by the term continuous random variable
- explain what is meant by the term continuous probability distribution
- use two continuous distributions which are important to engineers

#### Contents

1 Continuous probability distributions1.1 Continuous random variables

1.2 Definition

1.3 Practical example

1.4 The cumulative distribution function

1.5 Mean and variance of a continuous distribution

1.6 Important continuous distributions