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
Definition D5103
Unsigned basic expectation
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to [0, \infty]$ is a D5101: Random unsigned basic number on $P$
The expectation of $X$ on $P$ is the D1699: Basic number \begin{equation} \mathbb{E}_{\mathbb{P}} X : = \int_{\Omega} X \, d \mathbb{P} \end{equation}
Children
▶ D5102: Basic expectation
Results
▶ R3595: Probabilistic Tonelli's theorem
▶ R5301: Random unsigned basic number has zero correlation with the empty indicator
▶ R3517: Unsigned basic expectation zero iff random number almost surely zero