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Math Help - mgf of a discrete random variable

  1. #1
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    mgf of a discrete random variable

    A discrete random variable has pdf p(y)=bk^y, y=0,1,2,...
    Find Y's mgf m(t) generally.

    I get a bit stuck on what to do..
    I know that m(t)=E(e^{ty})
    so m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot p(y)which is equal to
    m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot bk^y but I'm not too sure how to expand this out...

    thanks for any help!
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  2. #2
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    Hello,
    Quote Originally Posted by Robb View Post
    A discrete random variable has pdf p(y)=bk^y, y=0,1,2,...
    Find Y's mgf m(t) generally.

    I get a bit stuck on what to do..
    I know that m(t)=E(e^{ty})
    so m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot p(y)which is equal to
    m(t)=\sum^{\inf}_{y=0}e^{ty}\cdot bk^y but I'm not too sure how to expand this out...

    thanks for any help!
    You're almost there
    Note that e^{ty}=(e^t)^y

    Thus e^{ty}\cdot bk^y can be written as b(ke^t)^y
    And this is a geometric series
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  3. #3
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    Thanks for that moo, i thought it was somethign similiar..
    so m(t)=\frac{b}{1-ke^t}

    the question also wants the mgf to be sketched when b=k=0.5 and to show the points t=0, t=0.2. I am a little bit confused, as to what the significance / point of drawing these points on the graph shows, and also the significance of the mgf graph? ie. i know about area under F(y) and f(y).. just wondering if there is a similiar significance for an mgf?
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