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Math Help - Probability generating function

  1. #1
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    Probability generating function

    Can someone show me the way how to solve below questions?
    Xi : independent identically distributed discrete random variables.
    N : positive random variable
    Xi 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.
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  2. #2
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    Re: Probability generating function

    Quote Originally Posted by sinvaldec View Post
    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.
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