Probability Theory: Random Variables and Independence

This lecture covers the concepts of discrete and continuous random variables, probability mass functions, and independence of random variables. It explains how to define the probability law of a variable, its cumulative distribution function, and the importance of independent variables. The instructor illustrates the concept of independence through examples and emphasizes the significance of independent and identically distributed variables. Additionally, the lecture delves into probability density functions, binomial random variables, and their mass functions. It concludes with a discussion on the properties of probability mass functions and the characteristics of binomial variables.