Introduction to Probability: Data and Uncertainty

This module provides an overview of the course structure, introduces key concepts in probability, and addresses frequently asked questions. It serves as a foundation for the upcoming units.

This module covers fundamental concepts of probability, counting techniques, and introduces story proofs as a method for solving probability problems. Students will learn how to calculate probabilities for various scenarios.

This module explores conditional probability and Bayes' Rule, essential concepts for analyzing complex probabilistic situations. Students will learn how to update probabilities based on new information and solve problems involving dependent events.

This module introduces discrete random variables and their properties. Students will learn about probability mass functions, expectation, and variance for discrete distributions, as well as common discrete probability distributions used in statistics.

This module covers continuous random variables and their properties. Students will learn about probability density functions, cumulative distribution functions, and important continuous probability distributions used in various fields.

This module explores key concepts in probability theory, including averages, the Law of Large Numbers, and the Central Limit Theorem. Students will learn about the behavior of sample means and the importance of these theorems in statistical inference.

This module covers joint probability distributions and conditional expectation. Students will learn how to work with multiple random variables simultaneously and understand the concept of expected value given certain conditions.

This module introduces Markov chains, a type of stochastic process with applications in various fields. Students will learn about state transitions, stationary distributions, and how to analyze systems that evolve over time according to certain probabilistic rules.