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Math Help - Poisson distribution problem

  1. #1
    Member
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    Nov 2011
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    Poisson distribution problem

    Hi all, hope you are having a fine day

    My problem is:

    Let X and Y be independent Poisson distributed stochastic variables, with expectation values
    5 and 10, respectively. Calculate the following probabilities:

    X + Y > 10

    What I have done to solve it:

    I found the Poisson probabilities when r = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 for both X and Y, then I added them all together, and subtracted them from 1. I keep getting the wrong answer, and my answer is over 1, which is a bit strange. The answer key says the correct answer should be: 0,882

    Thanks!
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  2. #2
    MHF Contributor
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    Re: Poisson distribution problem

    Hey Nora314.

    Hint: Write down all possible pairs of values where X + Y <= 10 and use the fact that P(A = a, B = b) = P(A=a)*P(B=b) for independent random variables A and B (with corresponding events a and b respectively).

    To keep track of things, I suggest you write the pairs with the corresponding probability.

    After this, you should be able to get the final answer.
    Thanks from Nora314
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