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Variance

September, 2026

Variance is the average of the square of the distance from the mean (Expectation).

Rules

Va r [a R] = a^{2} Va r [R]

Va r [R + b] = Va r [R]

σ_{a R + b} = ∣ a ∣ σ_{R}

Va r [R + S] = Va r [R] + Va r [S]

[T] If $X$ is a random variable with Binomial distribution then

Va r [X] = n \cdot p \cdot (1 - p)