probability theory: Quick Facts

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Photos

sample space for a pair of dice

A diagram illustrating Bayes's theorem using a group of 10,000 intravenous drug users, showing 2,500 are infected with HIV and 7,500 are not; within those tested, 2,375 true positives and 30 false positives are highlighted to demonstrate conditional probability.

probability density function

normal approximation to the binomial distribution

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Topics

statistical independence relative frequency interpretation subjective probability conditional expectation law of total probability gambler’s ruin 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

Engraving portrait of Carl Friedrich Gauss wearing a cap and formal 19th-century clothing, with detailed shading around his face and upper body.

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

Siméon-Denis Poisson

French mathematician

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Abraham de Moivre

French mathematician

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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

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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

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Richard von Mises

American mathematician

Blackwell, David

David Blackwell

American statistician and mathematician

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Francis Ysidro Edgeworth

Irish economist

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Hans Reichenbach

American philosopher

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