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Find joint pmf of X and X+Y

  • Thread starter chili237
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  • #1
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Homework Statement



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)

Homework Equations


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

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 :)
 

Answers and Replies

  • #2
Office_Shredder
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Science Advisor
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If X=k and X+Y=n then Y=?
 

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