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Math Help - moment generating function question

  1. #1
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    moment generating function question

    find the moment generating function of f(x)= 2^(-x) , x= 1,2,3,....
    Last edited by CaptainBlack; November 23rd 2010 at 03:25 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by omoboye View Post
    find the moment generating function of f(x)= 2^(-x) , x= 1,2,3,....
    M_X(t)=E(e^{tx})

    .......... \displaystyle = \sum_{x=1}^{\infty}e^{tx}2^{-x}=\sum_{x=1}^{\infty}e^{tx}e^{-x\ln(2)}

    which for t<\ln(2) is a convergent geometric series.

    CB
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