Convergence in Distribution

This lecture introduces the concept of convergence in distribution for random variables, which is a fundamental result in probability theory. The instructor explains how a sequence of random variables can converge in distribution, focusing on the convergence of their individual distributions. The lecture covers the definition of convergence in distribution, its relation to other types of convergence, and provides a formal proof of its properties. The instructor highlights the importance of this weaker notion of convergence and its applications in analyzing the asymptotic behavior of sums of random variables.