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
▼ Basic expectation
▼ Random real number moment
▼ Random real number central moment
▼ Absolute central moment
▼ Random real number variance
▼ Index of dispersion
Definition D5277
Index of variation
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}
The index of variation of $X$ is the D993: Real number \begin{equation} \frac{\sqrt{\text{Var} X}}{\mathbb{E} X} \end{equation}