Thread: Probability generating function

Can someone show me the way how to solve below questions?
X_i : independent identically distributed discrete random variables.
N : positive random variable
X_i and N are all mutually independent.
How can i define the random sum as

And how i can compute the probability generating function of S.

Originally Posted by sinvaldec

Can someone show me the way how to solve below questions?
How can i define the random sum as

I don't understand that question. You just have defined it...

And how i can compute the probability generating function of S.

Compute the PGF conditional on N and then use the law of iterated expectations.