Modes of Convergence of Random Variables

This lecture covers the modes of convergence of random variables, including Xm → x if tεdo, Xmªx if P A :) = `, Xm₂ ²³ X if FE[(xu, P(|Xu-x17E) 10, Xm ²³xx of Fxx (x Fx G) for all x where FxGx) is continuous. Implications and Lemmas are discussed to understand the convergence. The lecture also delves into the Central Limit Theorem and the Streng Law of Large Numbers, providing insights into approximations and probabilities involving sums of independent random variables.