01Module 3 - Probability Theory OverviewHow probability theory underpins every machine learning algorithm - from loss functions to generative models to uncertainty quantification.02Probability Axioms and EventsKolmogorov axioms, sample spaces, events, conditional probability, and independence - the formal foundations of all probabilistic reasoning in machine learning.03Random Variables and DistributionsDiscrete and continuous random variables, PMFs, PDFs, CDFs, and transformations - the formal tools for describing model outputs as probability distributions.04Expectation, Variance, and MomentsExpected value, linearity of expectation, variance, covariance, and higher moments - the summary statistics that define how ML models behave over data distributions.05Common Probability DistributionsBernoulli, Binomial, Multinomial, Gaussian, Exponential, Beta, Dirichlet - the probability distributions that appear throughout machine learning and which model outputs them.06Conditional Probability and Bayes' TheoremConditional probability, Bayes' theorem, prior and posterior, total probability - the engine behind Naive Bayes, Bayesian inference, and generative vs discriminative model design.07Joint and Marginal DistributionsJoint distributions, marginalization, conditional distributions from joint, independence, covariance matrices, and their role in graphical models and latent variable models.08Concentration InequalitiesMarkov, Chebyshev, and Hoeffding inequalities, the Central Limit Theorem, and the Law of Large Numbers - bounding probabilities and understanding generalization in machine learning.09Sampling MethodsInverse CDF, rejection sampling, importance sampling, MCMC, and Monte Carlo integration - the algorithms that power Bayesian inference, data augmentation, and generative modeling.
