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