Question

Find the joint pmf of two independent poissonally distributed random variables X and Y where

μ₁ = μ_x and μ₂ = μ_y. Then evaluate P(X + Y = 5).

Answer 1

 pmf of X+Y:

$f=P(X+Y=K)=\frac{(\mu_x+\mu_y)^ke^{-\mu_x-\mu_y}}{k!}$

$P(X+Y=5)=\frac{(\mu_x+\mu_y)^5e^{-\mu_x-\mu_y}}{5!}$