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.

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Originally Posted by sinvaldec

Can someone show me the way how to solve below questions?
How can i define the random sum as
http://quicklatex.com/cache3/ql_2c59...38f5247_l3.png

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

Quote:

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

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