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Thread: Last moment-generating function

  1. March 27th 2008, 08:41 PM #1
    TheHolly
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    Last moment-generating function

    This is the last of the moment-generating function problems that I do not understand for our homework. Any help would be greatly appreciated. Thanks!

    Given the moment-generating function Mx(t) = e{^{3t+8t{^2}}}, find the moment generating function of the random variable Z = {\frac{1}{4}}(X - 3), and use it to determine the mean and variance of Z.
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  2. March 27th 2008, 09:28 PM #2
    heathrowjohnny
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    M_{aX+b} = e^{bt}M_{X}(at)

    Then M'_{aX+b}(0) = \mu and E[Z^2] = M''_{aX+b}(0) and so \text{Var}(Z) = E(Z^2) - \mu^2 .
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