The digital textbook on probability and statistics
StatLect is a free digital textbook on probability theory and mathematical statistics. Explore its main sections.
Review the basics of differentiation and integration, learn about the fundamental concepts of combinatorial analysis, such as permutations and combinations; discover some special functions used in statistics.
Fundamentals of probability theory
Read a rigorous yet accessible introduction to the main concepts of probability theory, such as random variables and random vectors, expected value, variance, correlation, conditional probability and conditional expectation.
Additional topics in probability theory
Learn more advanced topics in probability theory, such as convolutions, transformations of random vectors, the moment generating function and the characteristic function.
Explore this compendium of common probability distributions, including the binomial, Poisson, uniform, exponential and normal distributions; find step-by-step derivations of the properties of the main probability distributions.
Learn about stochastic convergence, including convergence in probability, almost surely and in distribution; read about the Central Limit Theorem and the Law of Large Numbers.
This is a rigorous introduction to the basics of mathematical statistics; learn about statistical inference, point estimation, interval estimation and hypothesis testing.
Glossary of probability and statistics terms
Use this glossary to quickly review the technical terms that are introduced in the digital textbook.
Most learning materials found on this website have been collected in a single volume and are now available in a traditional textbook format.