Advanced Probabilities: Random Variables & Expected Values

This lecture covers advanced topics in probabilities, focusing on random variables, expected values, and variance calculations. It includes discussions on Bernoulli trials, probability mass functions, and the linearity of expectation. Students will learn to calculate probabilities for random variables and understand the distribution of random variables. The lecture also delves into the concept of variance and its characterization, providing examples related to dice rolls and coin flips. Practical exercises and quizzes are used to reinforce the theoretical concepts, preparing students for in-depth evaluations and exams.