Suppose X and Y are independent Poisson random variables,

[TomJerry]

Suppose X and Y are independent Poisson random variables, each with mean 1, obtain
i) P(X+Y)=4
ii)E[(X+Y)^2]


I m trying to solve this problem but have difficulty starting ... If some one could give me a some pointers

 

[grief]

i)What do you know about the sum of independent Poisson variables? (Hint: It's also Poisson).
ii)Let Z=X+Y. How do you find E(Z^2) in terms of the mean and variance of Z, which you should know?