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Math Help - How do you use moment generating functions to find pdfs?

  1. #1
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    How do you use moment generating functions to find pdfs?

    We never went over this in class, and it's not in the book, but there were 3 problems like it on the exam, and I got all 3 wrong, and the prof doesn't give solutions.

    So, for instance, how do you use the fact that the moment generating function of the Gaussian is e^(mt+t^2sigma^2/2) to find the pdf for Z(n)=sqrt(n)*(xbar(n)-mu/sigma)?
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    We never went over this in class, and it's not in the book, but there were 3 problems like it on the exam, and I got all 3 wrong, and the prof doesn't give solutions.

    So, for instance, how do you use the fact that the moment generating function of the Gaussian is e^(mt+t^2sigma^2/2) to find the pdf for Z(n)=sqrt(n)*(xbar(n)-mu/sigma)?
    You can use the basic properties of MGF.

    M_{a + bX} = e^{at}M_X (bt)

    Then examine the resulting MGFs...
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