Hi, here's the question:

Let $\displaystyle X_1,X_2,...,X_n$ be independent r.v.s with the Poisson distribution of parameter $\displaystyle m > 0$.

Let $\displaystyle Y = (X_1 + ... + X_n)/n$. Find the support and probability mass function of the distribution of $\displaystyle Y$. Calculate $\displaystyle E[Y-m]$ and $\displaystyle E[(Y-m)^2]$.

Any help would be appreciated. Thanks.