Probability·Course
Probability & Statistics
Probability theory and mathematical statistics: probability spaces, random variables, distributions, CLT, and statistical tests
9
Modules
27
Articles
~3 h
Reading
IV
CLOs
§ 01 — 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 →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Probability Spaces
Construct probabilistic models and compute event probabilities
CLO II
Random Variables
Work with discrete and continuous distributions and compute moments
CLO III
Limit Theorems
Apply the law of large numbers and the central limit theorem
CLO IV
Mathematical Statistics
Construct parameter estimators and test statistical hypotheses
§ 03 — Practices