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
▶ D5917: Random real number standard error