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Math Help - Poisson and binomial

  1. #1
    Member roshanhero's Avatar
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    Poisson and binomial

    If X and Y are independent poisson variates,show that the conditional distribution of X+Y is a binomial.
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  2. #2
    MHF Contributor matheagle's Avatar
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    as usual this is incompete, are you conditioning on X,Y, X+Y....?

    Since the binomial is finite and the Poissons are infinite, my guess is that you want X|X+Y or Y|X+Y
    since these will be bounded

    In any case use P(A|B)=P(AB)/P(B).

    AND X+Y is Poisson.

    A similar example can be found at the end of....http://mathworld.wolfram.com/BinomialDistribution.html

    DO exactly what they did but at eq (66) use the Poisson and what I said about the sum of two indep Poissons.
    Last edited by matheagle; August 3rd 2009 at 11:32 PM.
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