Definition

\[S_n^2=\sum_{i=1}^{n}\frac{(X_i-\overline{X}_n)^2}{n-1}\]

Bias

\[bias(S_n^2) = E[S^2_n] - \sigma^2 = 0\]

Demonstration (not shown)

Consistency

\(S_n^2\) is consistent because it converges in probability to \(\sigma^2\)

Demonstration (not shown)