Dependence and Correlation

This lecture covers the concepts of dependence and correlation in probability and statistics. It starts by defining the joint moments and central moments of random variables. The lecture then delves into the calculation of covariance, correlation, and conditional expectations. Various examples are provided to illustrate these concepts, including scenarios involving linear and nonlinear dependence, independence, and conditional expectations. The limitations of correlation in inferring causation are also discussed, emphasizing the importance of understanding the underlying relationships between variables.