Introduction to continuous random variables

Student learning objectives

By the end of this chapter, the student should be able to:

• Recognize and understand continuous probability distribution functions in general.
• Recognize the uniform probability distribution and apply it appropriately.
• Recognize the exponential probability distribution and apply it appropriately.

Introduction

Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long distance telephone call lasts, weight, height, and temperature are just a few. Generally, for continuous random variables, the outcomes are measured, rather than counted. The field of reliability depends on a variety of continuous random variables.

Note that the values of discrete and continuous random variables can sometimes be ambiguous. For example, if $X$ is equal to the number of miles (to the nearest mile) you drive to work then $X$ is a discrete random variable. You count the miles. If $X$ is the distance you drive to work, then you measure values of $X$ and $X$ is a continuous random variable. How the random variable is defined is very important.

This chapter gives an introduction to continuous random variables and continuous probability distributions. There are many continuous probability distributions. We will be studying continuous distributions for several chapters and will use continuous probability throughout the rest of this course. We will start with the two simplest continuous distributions, the Uniform and the Exponential .