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Math Help - factorial moment generating function

  1. #1
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    factorial moment generating function

    Question is #3 in the attached pic. Please help!
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  2. #2
    MHF Contributor matheagle's Avatar
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    E(t^X)=\sum_{x=0}^n{n\choose x}t^xp^x(1-p)^{n-x}

    =\sum_{x=0}^n{n\choose x}(tp)^x(1-p)^{n-x}

    Use the binomial theorem

    (pt+(1-p))^n

    If you differentiate and let t=1, you will obtain E(X)=np.

    Differentiate a second time and let t=1 and you will find E(X(X-1))

    This should work well with the Poisson too.
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  3. #3
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    Thank you for the response. I have been trying to figure out what you mean about the differentiation. I don't know what to differentiate. Could you ne a little more specific? Thank you
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  4. #4
    MHF Contributor matheagle's Avatar
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    differeniate wrt t, then let t=1
    it says that in the problem


    I'm really busy grading exams this weekend
    plus I have a galley proof to review
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