Variance

The variance of a random variable $X$ is the expected value of the squared deviation from the mean of $X$. $Var(X)=\mathbb{E}[(X-\mu {)}^2]$ $Var(x)=\frac{{\sum }_i^N{w}_i(X-\mu {)}^2}{{\sum }_i^N{w}_i}$

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Properties:

Relation to Expected Value

$Var(X)=\mathbb{E}(X^2)-\mathbb{E}(X{)}^2$

Useful Equivalence

For any constant $a,b$: $Var(aX+b)=a^{2}Var(X)$