Hi,

given that:$\displaystyle S^2=\frac{1}{n-1}\sum_{i=1}^{n}(X_i-\overline X)^2$.

I want to show that $\displaystyle E[S^2]=\sigma^2$

However, when i reached: $\displaystyle \frac{n}{n-1}(\frac{1}{n}\sum_{i=1}^{n}E[X_i^2]-E[\overline X^2])$, i was puzzled on finding $\displaystyle E[\overline X^2]$?

Since $\displaystyle E[\overline X^2]=Var(\overline X) + [E(\overline X)]^2$ which variance should I use, s.r.s or i.i.d?

or maybe is there any better way to prove it?