ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
Theory
Zermelo-Fraenkel set theory
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Binary cartesian set product
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Measurable simple complex function
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Unsigned basic integral
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Basic expectation
Definition D2015
Random real number moment
Formulation 1
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) $p \in (0, \infty)$ is a D5407: Positive real number
(ii) \begin{equation} \mathbb{E} |X|^p < \infty \end{equation}
The moment of $X$ with respect to $p$ is the D993: Real number \begin{equation} \mathbb{E} X^p \end{equation}
Children
D2014: Random real number absolute moment
D2013: Random real number central moment