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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
 ▶ Index of dispersion ▶ Random real number standard deviation
Results
 ▶ Additivity of variance for a finite number of independent random real numbers ▶ Real variance partition into first and second moments ▶ Variance of a finite sum of random real numbers ▶ Weak law of large numbers for random real triangular arrays ▶ Weak law of large numbers for variance with weighted decay