Definition:Variance/Discrete/Definition 3

Definition

Let $X$ be a discrete random variable.

Let $\expect X$ be the expectation of $X$.

Then the variance of $X$, written $\var X$, is defined as:

$\var X := \expect {X^2} - \paren {\expect X}^2$

Also see

• Variance as Expectation of Square minus Square of Expectation

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 2.4$: Expectation: $(23)$