Central Limit Theorem

Definition

Let $X_1,\dots ,X_n$ be i.i.d. Random Sample from a distribution with mean $\mu$, variance ${\sigma }^2$, then $\frac{\overline{X}-\mu }{\sigma /\sqrt{n}}\stackrel{D}{\to }Z\sim N(0,1)$

For i.i.d random variables that have finite variance, the sample mean converges to Normal Distribution.