# Thread: [SOLVED] Sum of two Poissons

1. ## [SOLVED] Sum of two Poissons

Suppose X has the poisson pmf pX(n) = λnexp(-λ)/n!, n>=0 and λ=5
and Y has the poisson pmf
pY(n)=μnexp(-μ)/n! n>=0 and μ=7
Let Z=X+Y, find

1. pz(7)
2. Let A be the event that z=6. Find pY|A(4)

2. Originally Posted by essedra
Suppose X has the poisson pmf pX(n) = λnexp(-λ)/n!, n>=0 and λ=5
and Y has the poisson pmf
pY(n)=μnexp(-μ)/n! n>=0 and μ=7
Let Z=X+Y, find

1. pz(7)
2. Let A be the event that z=6. Find pY|A(4)
Are X and Y independent? If so, here's your starting point: Sum of two independent Poisson random variables

3. I think they are independent but the point is, I don't know how to apply the formula.

4. Originally Posted by essedra
I think they are independent but the point is, I don't know how to apply the formula.
Can you write down the pmf for Z? Where are you stuck with question 1?

For question 2, what is
pY|A(4)
meant to mean?

5. Originally Posted by mr fantastic
Can you write down the pmf for Z? Where are you stuck with question 1?

For question 2, what is

meant to mean?
Ok, I figured out.