(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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)

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 :)

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# Find joint pmf of X and X+Y

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