I am doing this quesiton right now and I don't even know how to start it up. I know that it's in relation to a sum of a random number of random variables, but I don't know how to continue on from that.
I've read my textbook and it states some definition for an MGF which is: $M_{y}(t) = \sum_{n=0}^{\infty} M_{X}(t)^n p_{N}(n)$ but it doesn't derive it, however, I think it relates to this question?
The question is as follows:
Hint: condition on the service time.