ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Simple map
▼ Simple function
▼ Measurable simple complex function
▼ Simple integral
▼ Unsigned basic integral
▼ Unsigned basic expectation
Definition D5102
Basic expectation
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to [-\infty, \infty]$ is a D4381: Random basic number on $P$
(ii) \begin{equation} \mathbb{E} |X| < \infty \end{equation}
The expectation of $X$ on $P$ is the D1699: Basic number \begin{equation} \mathbb{E}_{\mathbb{P}} X : = \mathbb{E}_{\mathbb{P}} X^+ - \mathbb{E}_{\mathbb{P}} X^- \end{equation}
Children
▶ D2015: Random real number moment
Results
▶ R4577: Countable indicator partition of complex expectation in terms of pullback events
▶ R5282: Expectation of a random fraction need not equal fraction of expectations
▶ R4777: Expectation of bounded random real number is within the bounding interval
▶ R3516: Signed basic expectation of almost surely zero random number is zero