ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
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▼ Zermelo-Fraenkel set theory
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▼ Measurable simple complex function
▼ Simple integral
▼ Unsigned basic integral
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▼ Basic expectation
▼ Random real number moment
▼ Random real number central moment
Definition D2141
Random real number skewness
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|^3 < \infty \end{equation}
The skewness of $X$ is the D993: Real number \begin{equation} \text{Skew} X : = \mathbb{E} [ (X - \mathbb{E} X)^3 ] \end{equation}