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Math Help - help with probability proof

  1. #1
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    help with probability proof

    hi, i need help with this one,
    by using Moment-generating function, show that :


    thanks to all!
    Last edited by adirh; March 11th 2009 at 03:49 AM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm not sure what the MGF has to do with this.
    If you compare the two densities you can see that the Chi-Square is a particular gamma.
    You can do the same thing with the MGFs, if you wish.
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  3. #3
    Moo
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    Hello,

    Quote Originally Posted by adirh View Post
    hi, i need help with this one,
    by using Moment-generating function, show that :


    thanks to all!

    \chi^2_n has the MGF G(t)=\frac{1}{\sqrt{(1-2t)^n}}=\frac{1}{(1-2t)^{n/2}}

    \Gamma(n,\lambda) has the MGF G(t)=\left(\frac{\lambda}{\lambda-t}\right)^n
    so \Gamma(n/2,1/2) has the MGF G(t)=\left(\frac{1/2}{1/2-t}\right)^{n/2}=\left(\frac{1}{1-2t}\right)^{n/2}

    and this is the same as above
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  4. #4
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    first of all thanks for helping!

    but...

    the MGF for the gamma distribution (according to wikipedia) is:


    and not as you mentioned...
    and in this case the equaliy holds only for




    and not as asked..
    how can i solve this??
    thanks again!
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  5. #5
    Moo
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    There's sometimes a problem, as to know whether the second parameter of the Gamma distribution is \theta or \frac 1 \theta

    From the book I have, it said that the MGF is like I wrote above.

    So now it depends on how your teacher usually defines the second parameter.
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  6. #6
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    Oh... my lecturer (she's not a teacher ) uses my version of the MGF,
    so any ideas on how to solve it this way???
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