Definition:Variance/Discrete/Definition 2

Definition

Let $X$ be a discrete random variable.

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

$\ds \var X := \sum_{x \mathop \in \Omega_X} \paren {x - \mu^2} \map \Pr {X = x}$

where:

$\mu := \expect X$ is the expectation of $X$

$\Omega_X$ is the image of $X$

$\map \Pr {X = x}$ is the probability mass function of $X$.

Also see

• Equivalence of Definitions of Variance of Discrete Random Variable

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 2.4$: Expectation: $(22)$