- #1
chili237
- 3
- 0
X~Pois(λ)=> px(k)=e-λλk/k!
Y~Pois(μ)=> py(k)=e-μμk/k!
Find pX,X+Y(k,n)=P(X=k, X+Y=n)
...I know the pmf for X+Y ~ Pois(λ+μ)
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 :)
Y~Pois(μ)=> py(k)=e-μμk/k!
Find pX,X+Y(k,n)=P(X=k, X+Y=n)
...I know the pmf for X+Y ~ Pois(λ+μ)
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 :)