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Moment Generating Function

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  • Moment Generating Function

    Is it really necessary to memorize every moment generating function for each probability distribution?

  • #2
    I don't think it is necessary to memorize the moment generating
    functions of the various distributions. There have been, however, a couple
    of situations in which it might be possible to solve a problem a
    little faster if a distribution could be identified from the moment
    generating function.

    For example, if you are given a moment
    generating function and asked to find the distribution variance,
    you would find the first and second moments from the mgf
    in the usual way by taking first and second derivative of the mgf
    M'(t) and M"(t) and evaluating M'(0)=E[X] and M"(0)=E[X^2] ,
    and finally Var[X] = E[X^2] - (E[X])^2 . If you happened to
    recognize that the mgf was from a specific distribution, say
    Poisson and you can identify the Poisson parameter from
    the mgf, then Var[X] is the Poisson parameter.

    I think that the marginal benefit of knowing the mgf's
    makes knowing them a somewhat low priority for
    preparation for the exam. On the other hand, the more
    you know ...
    Sam Broverman

    [email protected]
    www.sambroverman.com

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    • #3
      Thx

      Thanks for the awesome reply

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      • #4
        yeah,

        but this September there was a number asking you to find a MGF of a gamma distribution which you could solve in 2 sec if you recognize it.

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