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Math Help - What's a gamma distribution and how does one apply an mgf to it?

  1. #1
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    What's a gamma distribution and how does one apply an mgf to it?

    Apply the m.g.f. of the gamma distribution to find its expectation and variance. Any help will be very much appreciated thank you so much.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Do you mean OBTAIN the mgf of a gamma?
    That's been done here before.
    Just combine the exponential terms and observe the new beta (so it's a valid density)
    and you're done.
    Last edited by matheagle; October 23rd 2009 at 09:41 PM.
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  3. #3
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    Well, if you are given the mgf, M(t), then
    E[X]=\frac{d}{dt}M(0)
    and
    Var(X)=E[X^2]-(E[X])^2=\frac{d^2}{dt^2}M(0)-(E[X])^2

    If you are not given the mgf, then you have to calculate
    M(t)=\int_{- \infty}^{\infty}e^{tx}f(x)dx where f(x) is the pdf of the gamma distribution
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