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## Homework Statement

X~Pois(λ)=> p

_{x}(k)=e

^{-λ}λ

^{k}/k!

Y~Pois(μ)=> p

_{y}(k)=e

^{-μ}μ

^{k}/k!

Find p

_{X,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 :)