Let $X_1, X_2, X_3, \ldots \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that

(i)	$X_1, X_2, X_3, \ldots$ is an D3357: Identically distributed random collection
(ii)	$X_1, X_2, X_3, \ldots$ is an D3842: Uncorrelated random collection
(iii)	\begin{equation} \mathbb{E} |X_1|^2 < \infty \end{equation}
(iv)	\begin{equation} \sigma^2 : = \text{Var} X_1 \end{equation}
(v)	$N \in \{ 2, 3, 4, \ldots \}$ is a D5094: Positive integer
(vi)	\begin{equation} \overline{X}_N : = \frac{1}{N} \sum_{n = 1}^N X_n \end{equation}

Then \begin{equation} \mathbb{E} \left( \frac{1}{N - 1} \sum_{n = 1}^N |X_n - \overline{X}_N|^2 \right) = \sigma^2 \end{equation}