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Math Help - Gamma-Poisson relationship.

  1. #1
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    Gamma-Poisson relationship.

    If X is a gamma distribution with parameter If X is a gamma distribution with parameter 3 and λ. i.e. X~Gamma(3,λ),
    then for any x,

    p(X≤x)=P(Y>3),

    where Y~Poisson(λx). (1)

    (a) Verify that equation (1) is true by successive integration by parts.
    (b) Express quation (1) as a probablistic relationship between Poisson process and its waiting time.
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  2. #2
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    Re: Gamma-Poisson relationship.

    Hey perh.

    Hint: Start with the integral definition on the left and use the hints to get an integral corresponding to the right hand side. (In other words start off with P(X <= x) and integrate by parts to get P(Y > 3) = 1 - P(Y < 3).
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