Central Limit Theorem: Proof and Applications

This lecture covers the Central Limit Theorem (CLT) proof and its applications. It starts by introducing the Strong Law of Large Numbers (SLLN) and then delves into the CLT, discussing weak convergence and the distribution of random variables. The instructor demonstrates the CLT proof using characteristic functions and explores the implications of independence in the context of the theorem. Various computations and approximations are presented to illustrate the concepts, providing a comprehensive understanding of the CLT and its significance in probability theory.