Hello,

Awww your notations are really awful !!! Pay more attention to what you are writing, you're not making any effort...

First simplify your solution to the first equation, because q=1-p, you simply get that s is 0 or 1.

If follows a , then compute the new generating function, by first conditioning it by , then by taking the expectation of the result. That's one basic property of conditional expectations.