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