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

http://quicklatex.com/cache3/ql_2c59...38f5247_l3.png

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

Re: Probability generating function

Quote:

Originally Posted by

**sinvaldec**

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

Quote:

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.