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Math Help - Probability Function

  1. #1
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    Probability Function

    Let Y1 and Y2 be independent Poisson random variables with means x1 and x2 respectively. Find the

    a) probability function of Y1 + Y2

    b) conditional probability function of Y1, given that Y1 + Y2 = m

    Please help. I will greatly appreciate it!! Thanks
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Let Y1 and Y2 be independent Poisson random variables with means x1 and x2 respectively. Find the

    a) probability function of Y1 + Y2

    b) conditional probability function of Y1, given that Y1 + Y2 = m

    Please help. I will greatly appreciate it!! Thanks
    Here is (a). (b) is left for you to do.



    (since the events are disjoint, that is, mutually exclusive)



    (using independence)



    (using the pmf of a Poisson random variable)







    (using binomial theorem)

    which is recognised as the pmf of a Poisson random variable with parameter .
    Last edited by mr fantastic; April 21st 2011 at 11:57 PM. Reason: Fixed latex.
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