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Math Help - moment generating function

  1. #1
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    moment generating function

    Hi i have a pdf in which i have to produce the mgf for.
    now i understand what the mgf is and how to use it to produce E(X) and var(X) and so on. but i struggle with the actual process of creating it.

    i would be very grateful if anyone could show a simple example for a continuous distribution explaining the steps involved

    thanks
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  2. #2
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    They key to doing the moment generating functions in my experience was to combine the e^{tx} term with the rest of your function so it can be factor out of the integral or it can be turned into a recognizable integral. I am no master on them, as we only did them in class for some simple distributions, but if you told me which distribution you wanted help with I might be able to help.

    Also check mathworld, there is tonnes of clarifications on how to derive MGF's.
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  3. #3
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    it is a transformed exponential distribution

    looks like this: f(x) = [x exp(-x^2)]/2

    my main problem with mgf's is that i dont understand how to get rid of the x
    Last edited by gvidfhi; December 8th 2008 at 02:14 PM.
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  4. #4
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    Quote Originally Posted by gvidfhi View Post
    it is a transformed exponential distribution

    looks like this: f(x) = [x exp(-x^2)]/2

    my main problem with mgf's is that i dont understand how to get rid of the x
    First of all, the pdf you've posted is wrong since it doesn't integrate to 1.

    You probably meant f(x) = x exp(-[x^2]/2), or, using latex and being precise in the definition:


    f(x) = x e^{-x^2/2} for x \geq 0 and zero elsewhere.


    Then m(t) = E(e^{tX}) = \int_0^{+\infty} e^{tx} \, x \, e^{-x^2/2} \, dx.

    Note: The answer to this cannot be found in terms of elementary functions. Where has your transformed pdf come from? Why do you require its mgf?
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