X is dist. Poisson with mean A, where A is moderately large.

You are given that Y = $\displaystyle X^2$

What is the mean of Y in terms of A?

I know this should be really simple, and I could do it is X was continuous, but how would I approach this, given that X is discrete? I'm sure I'm missing something really obvious here :/

E(Y) = E($\displaystyle X^2$) = ...?