Let $r_{i}$, for $i=1,2, \ldots, n$, be independent samples of a return $r$ of mean $\bar{r}$ and variance $\sigma^{2}$. Define the estimates

\[\begin{aligned}\hat{\bar{r}} & =\frac{1}{n} \sum_{i=1}^{n} r_{i} \\s^{2} & =\frac{1}{n-1} \sum_{i=1}^{n}\left(r_{i}-\hat{\bar{r}}\right)^{2} .\end{aligned}\]

Show that $\mathrm{E}\left(s^{2}\right)=\sigma^{2}$.