Application of Law of large numbers Could you give me hints on solving the question below?
Let $X_i$'s be iid r.v. Assume that they are mean zero ($EX_i$ = $0$) and they have finite variance. Consider $\bar{X_n} = \sum_{i = 1}^{n} \frac{X_i}{n}$. 
The goal is to show that $\sum_{i = 1}^{n} \frac{(X_i - \bar{X_n})^2}{(n - 1)} \rightarrow \sigma^2 \text{ almost surely as n} \rightarrow \infty$

1) Expand the square.
2) Notice that the strong law of large numbers can be applied to both $\{X_i\}$ and $\{X_i^2\}$.
