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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 $\sum_{i = 1}^{n} \frac{(X_i - \bar{X_n})^2}{(n - 1)} \rightarrow \sigma^2 \text{ almost surely as n} \rightarrow \infty$

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Got something from the answer? –  Did Sep 20 '13 at 18:03
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1 Answer

1) Expand the square.

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

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