Central Limit Theorem

CLT - Informal

Any sum of mutually independent, (identically distributed) random variables $X_1,…,X_k$ with mean $\mu$ and finite variance $\sigma^2$ converges to a Gaussian random variable with mean $k \cdot \mu$ and variance $k \cdot \sigma^2$, as $k \rightarrow \infty$. $$S = \sum_{i=1}^k X_i \implies \mathcal(k \cdot \mu, k \cdot \sigma^2)$$

References:

1. https://math.mit.edu/~sheffield/2018600/Lecture22.pdf