Underdispered random basic real number

▾ 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

Underdispered 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 underdispered if and only if \begin{equation} \frac{\text{Var} X}{\mathbb{E} X} < 1 \end{equation}