Lindeberg-Levy CLT

A special case of the Lindeberg-Feller CLT for iid random variables with finite variance.

Let $X_1,X_2,\dots$ be iid with mean $\mu$ and variance ${\sigma }^2<\infty$. Then

$$\sqrt{n}\left(\frac{\frac{1}{n}{\sum }_{i\le n}{X}_i-\mu }{\sigma }\right)\to N(0,1),$$

This follows from the Lindeberg condition the Lindeberg-Feller CLT.