Probability·Course
Probability & Statistics
Probability theory and mathematical statistics: probability spaces, random variables, distributions, CLT, and statistical tests
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Set up probability spaces correctly.
- 02Work with random variables and distributions.
- 03Use the limit theorems (LLN, CLT).
- 04Do real statistical inference.
- 05Tell a sound statistical claim from a bogus one.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~3 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Probability & Statistics [Online course]. Stoa. https://stoa.school/course/probability
- MLA
Stoa. “Probability & Statistics.” Stoa, 2026, https://stoa.school/course/probability.
- Chicago
Stoa. “Probability & Statistics.” Stoa. Accessed September 1, 2026. https://stoa.school/course/probability.
§ 02 — Curriculum
9 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IAxiomatic Foundations of Probability TheoryKolmogorov axioms, probability space, and classical probabilities3 articles
18 minBegin → - M IIRandom Variables and DistributionsDiscrete and continuous distributions, functions of random variables3 articles
18 minBegin → - M IIIExpectation and MomentsMoments, generating functions, inequalities, and the law of large numbers3 articles
18 minBegin → - M IVLimit TheoremsLaw of large numbers, central limit theorem, and large deviation theorems3 articles
18 minBegin → - M VSample Statistics and EstimationParameter estimation methods, nonparametric methods, and sufficient statistics3 articles
18 minBegin → - M VIStatistical Hypothesis TestingHypothesis testing criteria, regression analysis, and goodness-of-fit tests3 articles
18 minBegin → - M VIIStochastic ProcessesMarkov chains, Poisson process, martingales, and optimal stopping theory3 articles
18 minBegin → - M VIIIStochastic CalculusBrownian motion, Itô integral, Itô’s lemma, and stochastic methods in finance3 articles
18 minBegin → - M IXAsymptotic Statistics and RobustnessConvergence of estimators, Cramér–Rao bound, efficiency, and robust estimation3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Construct probabilistic models and compute event probabilities
Work with discrete and continuous distributions and compute moments
Apply the law of large numbers and the central limit theorem
Construct parameter estimators and test statistical hypotheses
§ 04 — Practices