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Find joint pmf of X and X+Y

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data

    X~Pois(λ)=> px(k)=eλk/k!

    Y~Pois(μ)=> py(k)=eμk/k!

    Find pX,X+Y(k,n)=P(X=k, X+Y=n)

    2. Relevant equations
    ....I know the pmf for X+Y ~ Pois(λ+μ)

    3. The attempt at a solution
    As I understand the joint pmf for two independent random variables would be the product of the two individual pmfs. However as X+Y is dependent on X I got really stuck trying to think about this one and how to set it up.

    Any help would be great. Thanks :)
  2. jcsd
  3. Nov 27, 2011 #2


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    If X=k and X+Y=n then Y=?
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