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
Random real number moment
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Absolute central moment
Random real number variance
Index of dispersion
Definition D5274
Overdispersed random basic real number
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \mathbb{E} |X|^2 < \infty \end{equation}
(ii) \begin{equation} \mathbb{E} X \neq 0 \end{equation}
Then $X$ is overdispersed if and only if \begin{equation} \frac{\text{Var} X}{\mathbb{E} X} > 1 \end{equation}