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
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}
Child definitions
» D3844: Index of dispersion
» D2144: Random real number standard deviation
» R4518: Equivalent characterisations of finiteness of variance for a random real number
» R3260: Weak law of large numbers for random real triangular arrays
» R4687: Additivity of variance for a finite number of independent random real numbers
» R4688: Second moment upper bound to real variance
» R2262: Real variance partition into first and second moments
» R3259: Weak law of large numbers for variance with weighted decay
» R2259: Variance of a finite sum of random real numbers