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Math Help - Moment Generating Functions

  1. #1
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    Moment Generating Functions

    So, the moment generating function of a random variable is a quick way to derive moments of the random variable through taking multiple derivatives and evaluating at t = 0.

    Is there ever an instance where you would evaluate it at some t other than 0? What is the significance of doing so?

    EDIT: I guess the I have the same question for joint distributions as well... I'm guessing they have similar significance but clearly the joint probabilities are a litttttle bit more complicated.


    Thanks,

    James
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  2. #2
    Moo
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    Re: Moment Generating Functions

    Hello,

    Think of the mgf as a sum, like here : Moment-generating function - Wikipedia, the free encyclopedia (the formula with 1+tm1+tēm2/2...). If you differentiate with respect to t, you'll get m1+tm2+... and so on. So if you don't set t=0, you'll have a residue that won't make you get the moments.
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