expectation

Long-run average value of a random variable

EntityQ200125

Also known as mathematical expectation · first moment · expected value · expectation value

Subclass of: arithmetic mean

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In probability theory, the expected value 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.

Overview

All data

33 statements · 12% with external sources · numbers in brackets are citations

Facet of: expectation
Defining formula: E[g(X)] = \int\limits_{\Omega} g(X) \mathrm{d} P
1
Sources
1.Stated in ISO 3534-1:2006(en) Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
View statement on Wikidata ↗
E[g(X)] = \int\limits_{\mathbb{R}^k} g(x) \mathrm{d} F(x)
1
Sources
1.Stated in ISO 3534-1:2006(en) Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
View statement on Wikidata ↗
In defining formula: E[g(X)] symbol represents: expectation
g symbol represents: function
X symbol represents: random variable
\Omega symbol represents: sample space
P symbol represents: probability
\mathbb{R} symbol represents: set of real numbers
F(x) symbol represents: distribution function
Different from: mean
Quantity symbol (LaTeX): E(\cdot)
E[\cdot]
Invariant under: Mean-preserving spread

On other databases

16 identifiers linking expectation across the web's reference databases

Data quality

statements

12%

externally sourced

Source last edited October 21, 2026. AIDB refreshes this page daily.

Suggest a fact or correction

Links

Use this data

curl https://aidb.si/api/v1/entities/Q200125

API docs, limits & keys

Cite this page

AIDB. (2026). expectation (Q200125). Retrieved from https://aidb.si/e/expectation-Q200125