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Math Help - Moment Generating Function

  1. #1
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    Moment Generating Function

    Differentiate the moment-generating function in Exercise 3.147 to find E(Y) and E(Y^2). Then find V(Y).

    Exercise 3.147

    If Y has a geometric distribution with probability of success p, show that the moment generating function for Y is

    m(t) = pe^t/(1-qe^t) , where q= 1-p

    Im confused... Differentiate with respect to what? After I take the derivative, how do I find E(Y), E(Y^2) and V(Y)?

    Thanks
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  2. #2
    Super Member Random Variable's Avatar
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    Differentiate with respect to t.

    Then E(Y) = m'(0), E(Y^2) = m''(0), and V(Y) = E(Y^2)-[E(Y)]^2 = m''(0) - [m'(0)]^2.
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