ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
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
Definition D2140
Random real number variance
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 variance of $X$ is the D4767: Unsigned real number \begin{equation} \text{Var} X : = \mathbb{E}|X - \mathbb{E} X|^2 \end{equation}
Index of dispersion
Random real number standard deviation
Additivity of variance for a finite number of independent random real numbers
Real variance partition into first and second moments
Variance of a finite sum of random real numbers
Weak law of large numbers for random real triangular arrays
Weak law of large numbers for variance with weighted decay