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Math Help - Geometric distribution

  1. #1
    Junior Member
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    Geometric distribution

    Hello everybody!
    Can you please help me with the following problem:

    Let ^ be random independent variables with geometric distribution.

    Find

    Please help me.
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  2. #2
    MHF Contributor
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    Re: Geometric distribution

    Which form of the geometric distribution are you using: \Pr(X = k) = (1-p)^{k-1}p for k = 1, 2, ..., or \Pr(X=k) = (1 - p)^kp for k = 0, 1, ...?

    In the first case, Pr(X = Y) = Pr(X = 1 /\ Y = 1) + Pr(X = 2 /\ Y = 2) + ... = Pr(X = 1)Pr(Y = 1) + Pr(X = 2)Pr(Y = 2) + ... since X and Y are independent. I believe this series is a geometric series.
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