probability theory

Table of Contents

Introduction
Experiments, sample space, events, and equally likely probabilities
- Applications of simple probability experiments
- The principle of additivity
- Multinomial probability
- The birthday problem
Conditional probability
- Applications of conditional probability
- Independence
- Bayes’s theorem
Random variables, distributions, expectation, and variance
- Random variables
- Probability distribution
- Expected value
- Variance
An alternative interpretation of probability
The law of large numbers, the central limit theorem, and the Poisson approximation
- The law of large numbers
- The central limit theorem
- The Poisson approximation
Infinite sample spaces and axiomatic probability
- Infinite sample spaces
- The strong law of large numbers
- Measure theory
- Probability density functions
Conditional expectation and least squares prediction
The Poisson process and the Brownian motion process
- The Poisson process
- Brownian motion process
Stochastic processes
- Stationary processes
- Markovian processes
- The Ehrenfest model of diffusion
- The symmetric random walk
- Queuing models
- Insurance risk theory
- Martingale theory

References & Edit History Related Topics

Images

sample space for a pair of dice

Bayes's theorem used for evaluating the accuracy of a medical test

probability density function

normal approximation to the binomial distribution

For Students

probability theory summary

Read Next

Galaxy clusters like Abell 2744 can act as a natural cosmic lens, magnifying light from more distant, background objects through gravity. NASA's James Webb Space Telescope may be able to detect light from the first stars in the universe if they are gravitationally lensed by such clusters. (astronomy, space exploration, galaxies)

How Fast Is the Universe Expanding?

Discover

M17, the Swan Nebula, is a star-making cloud in the constellation Sagittarius.

How Do We Know How Far Away the Stars Are?

Hindu Holi Festival celebrations with colored water, powder and colorful flower petals thrown over celebrants at a Hindu temple in Mathura, Uttar Pradesh, India on March 24, 2021.

Holi: Festival of Colors

A Factory Interior, watercolor, pen and gray ink, graphite, and white goache on wove paper by unknown artist, c. 1871-91; in the Yale Center for British Art. Industrial Revolution England

Inventors and Inventions of the Industrial Revolution

NBA Lakers Celtics Finals Kevin Garnett shooting.

10 Great Sports Rivalries

A mug shot taken by the regional Colombia control agency in Medellin

Pablo Escobar: 8 Interesting Facts About the King of Cocaine

Aphrodite. Greek mythology. Sculpture. Aphrodite is the Greek goddess of love and beauty.

12 Greek Gods and Goddesses

Florence, Italy Statue of David by Michelangelo

How a Rejected Block of Marble Became the World’s Most Famous Statue

probability theory: Related Content

Written and fact-checked by The Information Architects of Encyclopaedia Britannica

Photos

sample space for a pair of dice

Bayes's theorem used for evaluating the accuracy of a medical test

probability density function

normal approximation to the binomial distribution

See All Images →

Topics

Bayes’s theorem central limit theorem stochastic process indifference likelihood expected value statistical independence birthday problem gambler’s ruin relative frequency interpretation cryptology computer science combinatorics algebra statistics geometry automata theory set theory information theory trigonometry

Key People

Thomas Bayes

English theologian and mathematician

Andrey Andreyevich Markov

Russian mathematician

Carl Friedrich Gauss

Carl Friedrich Gauss

German mathematician

Fermat, portrait by Roland Lefèvre; in the Narbonne City Museums, France

Pierre de Fermat

French mathematician

Andrey Nikolayevich Kolmogorov, 1966.

Andrey Nikolayevich Kolmogorov

Russian mathematician

Siméon-Denis Poisson, detail of a lithograph by François-Séraphin Delpech after a portrait by N. Maurin.

Siméon-Denis Poisson

French mathematician

Abraham de Moivre

French mathematician

Pafnuty Lvovich Chebyshev.

Pafnuty Chebyshev

Russian mathematician

Quetelet, Adolphe

Adolphe Quetelet

Belgian astronomer, sociologist, and statistician

Paul Lévy

French mathematician

Rudolf Carnap

Rudolf Carnap

German-American philosopher

John Venn

John Venn

English logician and philosopher

Varadhan, S.R. Srinivasa

S.R. Srinivasa Varadhan

Indian mathematician

Richard von Mises

American mathematician

Francis Ysidro Edgeworth

Irish economist

Blackwell, David

David Blackwell

American statistician and mathematician

Hans Reichenbach

American philosopher

Quiz

Equations written on blackboard

Numbers and Mathematics

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

Define It: Math Terms