Convergence in Probability

This lecture covers the concept of convergence in probability, illustrated through examples of sequences of random variables converging in probability but not almost surely. It also explores concentration inequalities, Chebyshev's inequality, and the weak and strong laws of large numbers. The lecture delves into the properties of marginal and conditional distributions, Gaussian conditioning, and the calculation of conditional expectations and variances. Additionally, it discusses the moment-generating function, mixed moments formula, and the Gaussian vector. The instructor provides detailed explanations and proofs to deepen the understanding of these fundamental concepts in probability theory.