ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D2140
Random real number variance

Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
 (i) $$\mathbb{E} |X|^2 < \infty$$
The variance of $X$ is the D4767: Unsigned real number $$\text{Var} X : = \mathbb{E}|X - \mathbb{E} X|^2$$
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