# CLT

## Thirty isn't the magic number

The simplest version of the central limit theorem (CLT) says that if $$X_1, \dots, X_n$$ are iid random variables with mean $$\mu$$ and finite variance $$\sigma^2$$ $\frac{\bar{X}_n - \mu}{\sigma/\sqrt{n}} \rightarrow_d N(0,1)$ where $$\bar{X}_n = \frac{1}{n} \sum_{i=1}^n X_i$$.