## 3.1.2 Discrete Random Variables

There are two important classes of random variables that we discuss in this book: *discrete random variables*
and *continuous random variables*. We will discuss discrete random variables in this chapter and
continuous random variables in Chapter 4. There will be a third class of random variables that are called
*mixed random variables*. Mixed random variables, as the name suggests, can be thought of as mixture
of discrete and continuous random variables. We will discuss mixed random variables in Chapter 4 as well.

Remember that a set $A$ is countable if either

- $A$ is a finite set such as $\{1,2,3,4\}$, or
- it can be put in one-to-one correspondence with natural numbers (in this case the set is said to be countably infinite)

$X$ is a discrete random variable, if its range is countable.