Lecture 5: Probability Theory (cont.); Stochastic Processes I

Principal components analysis (PCA) is a statistical technique that transforms a random vector in a multidimensional space by shifting and rotating coordinates to identify orthogonal directions of maximum variability, often used in financial data to simplify complex covariance structures. Additionally, the discussion covers foundational probability concepts such as the central limit theorem, utility optimization in asset pricing, and introduces stochastic processes like martingales, highlighting their importance in modeling financial markets and solving probability problems.