Hi, I am having trouble trying to find the distribution and expectation.

Suppose X and Y are independent random variables each governed by the common Poisson distribution with mean 1. Suppose n is any given non-negative integer. (a) Evaluate the conditional distribution of X given that X + Y = n, that is to say, evaluate Pn (k) := P{X = k | X + Y = n} for each k. (b) Evaluate the conditional expectation E(X | X + Y = n)