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Math Help - find MGF given PMF

  1. #1
    Junior Member
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    Oct 2008
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    39

    find MGF given PMF

    I'm given pmf of X is (1/2)^(x+1) and asked to find the moment generating function.


    so i have MGF = sum{(exp(xt))*(1/2)^(x+1)}

    sum((1/2)^x) goes to 1.

    but the exp(x) either blows up or goes to 0 depending on t...

    I think i'm supposed to have a function of t left. Any errors here?

    Thanks
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  2. #2
    Junior Member
    Joined
    Jan 2007
    Posts
    42
    I am assuming you mean discrete geometric distribution with x = 0,1,2, ....

    on simplifying mgf = (1/2) ∑ [exp(t) / 2 ]^x where the summation is from 0 to infinity

    mgf = (1/2) / { 1 -[exp(t) / 2 ] } using the formulae for infinite geometric series (with suitable restriction on t as you said)

    note
    expand the ∑ and use 1 + u + uČ + . . . = 1 / (1-u) if |u| < 1

    here u = [exp(t) / 2 ]


    try the following page for mgf of binomial distribution
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