# What is a bounded discrete random variable

I'm reading a definition in DeGroot's book that begins with the statement:

"Let X be a bounded discrete random variable whose p.f. is f."

Then he goes on to define the expectation of X.

However, I cannot find a definition of what is meant by a "bounded" discrete random variable anywhere in the book (after an hour of looking). I do know what a discrete random variable is, but what does the word "bounded" mean in this case?

Thanks.

• Bounded just means that there exist a number $M>0$ such that $|X| \le M$ with probability 1. Jun 2, 2014 at 19:10

So, $P(Z > z)$ is never actually equal to zero for any finite z. [EDIT] This means that Z is unbounded.
$P(x < m) = 0$ and $P(x>M) = 0$