The complete Stanford CS109 course reader, rebuilt as interactive lessons. From counting to machine learning, with simulations at every step.
Step rule, permutations, combinations, binomial coefficients, stars & bars, multinomials.
Empirical definition, sample spaces, equally likely outcomes, complement, inclusion-exclusion.
Conditional probability, chain rule, independence, law of total probability, Bayes’ theorem.
Many coin flips, Enigma machine, birthday paradox, random shuffles, Gini impurity.
Definition, PMF, CDF, functions of RVs, indicator variables.
E[X], linearity, LOTUS, variance, standard deviation, properties.
Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, Categorical.
PDF, CDF, Uniform, Exponential, Normal, Z-scores, binomial approximation.
Joint PMF/PDF, marginalization, multinomial, covariance, correlation.
Bayes for RVs, MAP/MLE preview, Bayesian networks, conditional independence.
Inference framework, prior/posterior, likelihood, fairness in AI.
Beta as conjugate prior, convolution, Central Limit Theorem, proof sketch.
Random sampling, bootstrap CIs, entropy, KL divergence, information theory.