Let Y be a random variable that takes on positive integers.

Where

a) Find the probability that

b) Find the moment generating function of .

c) Find the first and second moments

Attempt:

(A)

I don't really know what to do with it. I understand that it is an infinite geometric series that will sum to 1. But I'm not sure how to find Y = 0.

Using the formula for geometric series, I can find various p(k) in terms of p(0), but I don't know how to find p(0) itself.

(B)

I'm I on the right track? I'm not sure how to proceed after that.

(C)

That just involves finding the first and second derivative of the result I find in B, correct?