Hello, I have recently enrolled in a 3rd year Introductory Probability course.
I'm having a pretty tough time with the course so I came to this forum again to seek some guidance.
When looking at geometric random variables I was asked to find the expected value of r^X, where X is a geometric rv.
I know that E(X) = Sum(n*(1-p)^(n-1)*p) in a geometric series... but it confuses me when I have to find E(r^X).
What do I have to do in this case?
It's not a matter of definition related to a geometric distribution. It's just that for any 'correct' function f and, for example, a discrete random variable X, with probability function p, we have :
If X takes integer and positive values. Otherwise, you'll have to change the range of k, but that's all.