Probability

Variance

Also known as: Var

The expected squared deviation from the mean, measuring how spread out a distribution is.

Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2.

That second form is the computational one and is worth memorising - it turns most variance calculations into two expectations.

Scaling: Var(aX) = a^2 Var(X). The square matters, and it is why doubling a position quadruples variance while only doubling expected profit.

For a sum, Var(X + Y) = Var(X) + Var(Y) + 2Cov(X, Y). The covariance term vanishes only when the variables are uncorrelated.

The trap. Variance is in squared units, which is why standard deviation is usually reported instead.

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