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

(i)	$X_1, \ldots, X_N$ is an D3357: Identically distributed random collection
(ii)	$F : \mathbb{R} \to [0, 1]$ is a D205: Probability distribution function for $X_1$

Let $x \in \mathbb{R}$ be a D993: Real number.

Then \begin{equation} \mathbb{E} \left( \frac{1}{N} \sum_{n = 1}^N I_{\{ X_n \leq x \}} \right) = F(x) \end{equation}