Expectation of a Random Variable

This lecture aims to define the expectation for a random variable, which is the theoretical notion of average. Starting with the definition for a simple function, the instructor explains how to extend it to non-negative and general functions. By breaking down the process into three steps, the lecture covers how to compute the expectation for various types of random variables, emphasizing the importance of the absolute value of the function. Through examples and illustrations, the lecture demonstrates how to calculate expectations for both discrete and continuous random variables, highlighting the significance of these calculations in probability theory.