Set of symbols
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Deduction system
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Zermelo-Fraenkel set theory
Set
Binary cartesian set product
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Simple map
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Measurable simple complex function
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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
Results
» 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