# [SOLVED] Sum of two Poissons

• Mar 28th 2009, 05:41 AM
essedra
[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)
• Mar 28th 2009, 01:23 PM
mr fantastic
Quote:

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
• Mar 28th 2009, 05:21 PM
essedra
I think they are independent but the point is, I don't know how to apply the formula.(Sadsmile)
• Mar 28th 2009, 06:14 PM
mr fantastic
Quote:

Originally Posted by essedra
I think they are independent but the point is, I don't know how to apply the formula.(Sadsmile)

Can you write down the pmf for Z? Where are you stuck with question 1?

For question 2, what is
Quote:

pY|A(4)
meant to mean?
• Mar 29th 2009, 02:59 AM
essedra
Quote:

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.