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Math Help - Moment generation function

  1. #1
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    Moment generation function

    Hi,

    I was given a moment generating function M(t) = (1-t)^-3

    However, I'm told to compute P (-5 < X < 4) if I can (or explain if I can't compute).

    ---

    If I'm not wrong the random variable (X) is gamma with parameters (2,1).

    But X must be at least 0. So does do I compute P (-5 < X < 4) = P (0 < X < 4) ? Or is it un-computable? If so, how do I explain?

    Can anyone help? Thanks.
    Last edited by knighty; April 3rd 2009 at 10:03 AM.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by knighty View Post
    Hi,

    I was given a moment generating function M(t) = (1-t)^-3

    However, I'm told to compute P (-5 < X < 4) if I can (or explain if I can't compute).

    ---

    If I'm not wrong the random variable (X) is gamma with parameters (2,1).

    But X must be at least 0. So does do I compute P (-5 < X < 4) = P (0 < X < 4) ? Or is it un-computable? If so, how do I explain?

    Can anyone help? Thanks.
    It's a Gamma, but I think it's rather (3,1) than (2,1) (I checked it in wikipedia )

    You're correct to say that P(-5<X<4)=P(0<X<4)
    You can even say that it's P(X<4), where X follows \Gamma(3,1)

    So you're looking for the value of the cumulative density function of Gamma(3,1) : F(4;3;1)=1-\sum_{i=0}^2 \frac{4^i}{i!} e^{-4}
    Look here : Gamma distribution - Wikipedia, the free encyclopedia
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