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Math Help - Gamma distribution mgf

  1. #1
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    Gamma distribution mgf

    Y has gamma distribution with α=n/2 for some positive integer n and β equal to some specified value. Using method of mgf, show that W=2Y/β has a chi-square dist. with n df.

    I know what the mgfs of gamma and chi-square are. The part that is confusing me is the W=2Y/β and how to plug in the mgf's and such.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Obtain the MGF of W.

    M_W(t)= E(e^{Wt})=E(e^{2Yt/\beta})=M_Y(2t/\beta)

    So, insert 2t/\beta where you have t in the MGF of Y.
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