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 D3842: Uncorrelated random collection
(ii)	\begin{equation} \exists \, \mu \in \mathbb{R} : \forall \, n \in 1, 2, 3, \ldots : \mathbb{E} X_n = \mu \end{equation}
(iii)	\begin{equation} \exists \, C \in [0, \infty) : \forall \, n \in 1, 2, 3, \ldots : \text{Var} X_n \leq C \end{equation}

Then

(1)	\begin{equation} \frac{1}{N} \sum_{n = 1}^N X_n \overset{L^2}{\longrightarrow} \mu \quad \text{ as } \quad N \to \infty \end{equation}
(2)	\begin{equation} \frac{1}{N} \sum_{n = 1}^N X_n \overset{p}{\longrightarrow} \mu \quad \text{ as } \quad N \to \infty \end{equation}