Central Limit Theorem: Empirical Mean

This lecture covers the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) applied to the empirical mean of Bernoulli and Uniform random variables. It explains the convergence in distribution, the CLT for i.i.d. random variables, and the multivariate version of the CLT. The slides illustrate the convergence of the empirical mean distribution around the true mean, emphasizing the Gaussian distribution. The continuous mapping theorem is also discussed in the context of the CLT.