ThmDex – An index of mathematical definitions, results, and conjectures.
F12965
Formulation 0
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) \begin{equation} \mathbb{E} |X_1| < \infty \end{equation}
(iii) \begin{equation} \mu : = \mathbb{E} X_1 \end{equation}
Then \begin{equation} \mathbb{E} \left( \frac{1}{N} \sum_{n = 1}^N X_n \right) = \mu \end{equation}