i need help on this questions i really do not understand it

Let X be a Poisson random variable with mean μ and let Y be a

Poisson random variable with mean μ. Assume that X and Y are independent.

(a) Write down the joint probability that X = i and Y = n−i, where n and i

are integers with 0 <i<n

(b) Calculate P(X + Y = n), where n is a non-negative integer.

(c) What distribution does the random variable X + Y have?