Given independent and identically distributed random variables $X_1, X_2, ..., X_n$
We know that the random variable $Y=\frac{1}{n}\sum{X_i}$ is normally distributed (from the Central Limit Theorem)
Given this information, can we figure out the mean $\mu$ and variance $\sigma^2$ of this normal $Y$ random variable?
If not, what if we're given $\mathbb E(X_i)$ and $Var(X_i)$ $\forall i$ ? Can we find out then?