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Expected value

In probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it is finite, the expected value can be interpreted as the long-run average of results from independent repetitions of the same random experiment, as formalized by the law of large numbers.

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Overview

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Definition

Expected values of common distributions

Properties

Uses and applications

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Map overview Semantic statistics

Expected value

Nodes129
Edges128
Triples125
Avg. degree1.98
Density0.015504
Components1

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Expected value

Top relations

related to Properties · 26
Expected value → As, Basically, Bernoulli, By, CDF, Formulas, If, In, Law, Lebesgue, Lebesgue-Stieltjes, Let, Linearity, Monotonicity, Non-degeneracy, Non-multiplicativity, Non-negativity, Note, Pr, Proof
related to history · 14
Expected value → Blaise Pascal, Chevalier, Fermat, French, He, Méré, Paris, Pascal, Pierre, Soon, The, They, This, While
related to Infinite expected values · 13
Expected value → According, Expected, Given, However, It, Lebesgue, Petersburg, Since, St, The, There, These, This
related to Arbitrary real-valued random variables · 11
Expected value → All, Borel, Despite, However, In, Lebesgue, Moreover, Omega, Sigma, The Radon-Nikodym, This
related to Inequalities · 11
Expected value → Chebyshev, Chebyshev's, Concentration, For, However, If, Markov, Markov's, The Kolmogorov, These, Var
related to Expectations under convergence of random variables · 9
Expected value → Analogously, But, For, Hence, In, Pr, Then, Thus, To
related to Notations · 9
Expected value → English, Erwartungswert, EX, French, In German, Spanish, The, When, Whitworth
related to Definition · 8
Expected value → All, Any, As, It, Lebesgue, Similarly, The, With
related to Etymology · 6
Expected value → Huygens, In, More, Neither Pascal, Pierre-Simon Laplace, Théorie
related to Random variables with countably infinitely many outcomes · 6
Expected value → However, In, Informally, Riemann, Since, This

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Important terminology

displaystyle random expected value operatorname variable expectation probability variables one values case given infty function theory finite lebesgue leq geq

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Expected valueis aweighted average of those values0.90text
Expected valueis alinear form on this vector space.Monotonicity0.90text
Expected valuehas applicationThe0.60section
Expected valuehas applicationIn0.60section
Expected valuerelated to Arbitrary real-valued random variablesAll0.60section
Expected valuerelated to Arbitrary real-valued random variablesIn0.60section
Expected valuerelated to Arbitrary real-valued random variablesOmega0.60section
Expected valuerelated to Arbitrary real-valued random variablesSigma0.60section
Expected valuerelated to Arbitrary real-valued random variablesLebesgue0.60section
Expected valuerelated to Arbitrary real-valued random variablesDespite0.60section
Expected valuerelated to Arbitrary real-valued random variablesThis0.60section
Expected valuerelated to Arbitrary real-valued random variablesMoreover0.60section

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