Introduction to Probability

Chapter 5

Continuous random variables

So far we have been working with discrete random variables, whose possible values can be written down as a list. In this chapter we will discuss continuous r.v.s, which can take on any real value in an interval (possibly of infinite length, such as (0, ∞) or the entire real line). First we’ll look at properties of continuous r.v.s in general. Then we’ll introduce three famous continuous distributions—the Uniform, Normal, and Exponential—which, in addition to having important stories in their own right, serve as building blocks for many other useful continuous distributions.

5.1 Probability density functions

Recall that for a discrete r.v., the CDF jumps at every point in the support, and is flat everywhere ...