Empirical Distribution Function

Definition

Let $X_i,i=1,2,\dots ,n$ be i.i.d. random variables with the Distribution Function $F(t)$, then the empirical distribution function is defined as ${\hat{F}}_n(t)=\frac{1}{n}\sum _{i=1}^{n}I(X_i\le t)$ Since $I(X_i\le t)$ is a Bernoulli trial, $n{\hat{F}}_n(t)\sim B(n,F(t))$