1. The problem statement, all variables and given/known data Show that if X is a bounded random variable, then E(X) exists. 2. Relevant equations 3. The attempt at a solution I am having trouble of finding out where to begin this proof. This is what I got so far: Suppose X is bounded. Then there exists two numbers a and b such that P(X > b) = 0 and P(X < a) = 0 and P(a <= X <= b) = 1. I have no idea if I am even doing this right. Anyone wanting to take a crack at this one? Thanks.