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, â) or the entire real line). First weâll look at properties of continuous r.v.s in general. Then weâll introduce three famous continuous distributionsâthe Uniform, Normal, and Exponentialâwhich, 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 ...