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

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probability theory summary

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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

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Topics

subjective probability law of total probability relative frequency interpretation statistical independence gambler’s ruin conditional expectation birthday problem Bayes’s theorem expected value central limit theorem cryptology computer science combinatorics algebra statistics geometry automata theory set theory information theory trigonometry

Key People

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

Andrey Andreyevich Markov

Russian mathematician

Pafnuty Lvovich Chebyshev.

Pafnuty Chebyshev

Russian mathematician

Quetelet, Adolphe

Adolphe Quetelet

Belgian astronomer, sociologist, and statistician

Understand how Bayes's theorem can make educated mathematical guesses when there is not much to go on

Thomas Bayes

English theologian and mathematician

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

Blackwell, David

David Blackwell

American statistician and mathematician

Francis Ysidro Edgeworth

Irish economist

Hans Reichenbach

American philosopher

Quiz

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

Define It: Math Terms

Equations written on blackboard

Numbers and Mathematics