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
Definition D2144
Random real number standard deviation
Formulation 2
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}
The standard deviation of $X$ is the D4767: Unsigned real number \begin{equation} \text{Std} X : = \left( \mathbb{E}|X - \mathbb{E} X|^2 \right)^{1/2} \end{equation}
Formulation 3
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}
The standard deviation of $X$ is the D4767: Unsigned real number \begin{equation} \text{Std} X : = \sqrt{ \mathbb{E}|X - \mathbb{E} X|^2 } \end{equation}
Children
Random real number standard error