Section 1: Probability Foundations
Overview
Focus on the core probability theory that underpins all of machine learning: axioms, random variables, distributions, and summary statistics.
Topics Covered
Chapter 1: Probability Basics
- Probability axioms and sample spaces
- Conditional probability and Bayes' theorem
- Independence and the law of total probability
Chapter 2: Random Variables
- Discrete and continuous random variables
- PMF, PDF, and CDF
- Transformations of random variables
Chapter 3: Common Distributions
- Bernoulli, Binomial, Poisson
- Gaussian, Exponential, Gamma, Beta
- Categorical, Multinomial, Uniform
Chapter 4: Expectation and Variance
- Expectation and its properties
- Variance, covariance, and correlation
- Moments and the law of the unconscious statistician
Learning Objectives
- State and apply the axioms of probability
- Use Bayes' theorem to update beliefs given evidence
- Work with common discrete and continuous distributions
- Compute expectations, variances, and covariances