Explore Bayes' Rule and maximum likelihood estimation through practical examples and mathematical derivations in this foundational data analysis lecture. Learn how to apply Bayes' Rule using a cracked windshield scenario to understand the concept of probability of a model given data. Work through detailed examples involving n data points in one dimension with normal noise assumptions, and discover how to derive the maximum likelihood estimate as the sum of squared errors, which simplifies to the average of the data. Master these fundamental statistical concepts that form the backbone of data analysis and machine learning through clear explanations and step-by-step mathematical proofs.