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
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}
Children
D3844: Index of dispersion
D2144: Random real number standard deviation
Results
R4687: Additivity of variance for a finite number of independent random real numbers
R2262: Real variance partition into first and second moments
R2259: Variance of a finite sum of random real numbers
R3260: Weak law of large numbers for random real triangular arrays
R3259: Weak law of large numbers for variance with weighted decay