Conditional Expectation: Basics

This lecture covers the basics of conditional expectation, including the definition, properties, and examples. It explains how to calculate conditional probabilities and expectations with respect to different events and random variables. The instructor discusses the concept of conditioning with respect to a sub-sigma-algebra and demonstrates the linearity and monotonicity properties of conditional expectation. Various examples illustrate the application of conditional expectation in the context of discrete and continuous random variables. The lecture concludes with a discussion on conditional expectation with sub-sigma-fields and the uniqueness of conditional expectations.