Introduction

Student learning objectives

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

• Recognize and understand continuous probability density functions in general.
• Recognize the uniform 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, the amount of money a person carries, thelength of time a computer chip lasts, and SAT scores are just a few. The field of reliability depends on a variety of continuous random variables.

This chapter gives an introduction to continuous random variables and the many continuous distributions. We will be studying these continuous distributions for several chapters.

The characteristics of continuous random variables are:

• The outcomes are measured, not counted.
• Geometrically, the probability of an outcome is equal to an area under a mathematical curve called the density curve, $f(x)$ .
• Each individual value has zero probability of occurring. Instead we find the probability that the value is between two endpoints.

We will start with a simplest continuous distributions, the Uniform .