Probability and Statistics
The mathematical foundation every ML practitioner needs.
01Probability and Statistics (1): Probability Spaces — Why We Need Axioms (But Won't Overdo It)
Building probability from the ground up: sample spaces, Kolmogorov's axioms, conditional probability, Bayes' theorem, …
02Probability and Statistics (2): Random Variables and the Distributions That Matter
A rigorous tour of random variables, PMFs, PDFs, CDFs, and every distribution that matters in practice — Bernoulli, …
03Probability and Statistics (3): Expectation, Variance, and the Moment-Generating Trick
From expectation and variance through covariance, correlation, and moment-generating functions to Chebyshev's inequality …
04Probability and Statistics (4): Joint Distributions, Marginalization, and Independence
Joint PMFs and PDFs, marginal and conditional distributions, the bivariate normal, transformations via the Jacobian …
05Probability and Statistics (5): Law of Large Numbers and the Central Limit Theorem
The two pillars of probability: the Law of Large Numbers guarantees sample means converge, and the Central Limit Theorem …
06Probability and Statistics (6): Estimation — MLE, MAP, and the Bias-Variance Story
Point estimation from method of moments through maximum likelihood and MAP, with Fisher information, the Cramer-Rao …
07Probability and Statistics (7): Hypothesis Testing — p-Values, Confidence Intervals, and All Their Pitfalls
A rigorous treatment of hypothesis testing, p-values, Type I/II errors, confidence intervals, and multiple testing …
08Probability and Statistics (8): Bayesian Statistics — Priors, Posteriors, and Why Frequentists Argue
Bayesian inference from first principles: posterior distributions, conjugate priors, the Beta-Binomial and Normal-Normal …