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Math Help - Poisson

  1. #1
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    Poisson

    If X~Po(2) and Y~Po(1). How to find P(X>Y)?
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  2. #2
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    Quote Originally Posted by syjytg View Post
    If X~Po(2) and Y~Po(1). How to find P(X>Y)?
    Are X and Y independent?
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  3. #3
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    Yes, X and Y are independent.
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  4. #4
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    Quote Originally Posted by syjytg View Post
    Yes, X and Y are independent.
    The joint pdf is f(k, l) = \left( \frac{e^{-2} 2^k}{k!} \right) \, \left( \frac{e^{-1} 1^l}{l!} \right) = \frac{e^{-3} 2^k}{k! \, l!}.

    \Pr(X > Y) = \sum_{k=1}^{\infty} f(k, 0) + \sum_{k=2}^{\infty} f(k, 1) + \sum_{k=3}^{\infty} f(k, 2) + \, ....
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  5. #5
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    Can you please complete it until you get the answer? I still do not know how to continue from here.

    I mean I do not know how to evaluate the expression you gave above.
    Last edited by syjytg; October 7th 2008 at 03:44 AM.
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