"Let Y_n be the number of trials up to and including the first success in a sequence of independent trials, where each trial has a probability of success of k/n.
Find the moment generating function of (1/n)Y_n. Hence show that, as n -> infinity, the limiting distribution of (1/n)Y_n is exponential with parameter k."
I should be able to manage the "deduction" part of the question providing that I can find the moment generating function of (1/n)Y_n in the first place. This is proving to be quite tricky for me though. How do we go about doing this? And then for the second part, presumably we can let n -> infinity in the moment generating function and spot that this gives the same generating function as an exponential with parameter k, and then appeal to uniqueness of generating functions? Thanks.