Editing Variance (section)

===Addition and multiplication by a constant===
Variance is [[Invariant (mathematics)|invariant]] with respect to changes in a [[location parameter]].  That is, if a constant is added to all values of the variable, the variance is unchanged:
<math display="block">\operatorname{Var}(X+a)=\operatorname{Var}(X).</math>

If all values are scaled by a constant, the variance is [[Homogeneous function|scaled]] by the square of that constant:
<math display="block">\operatorname{Var}(aX)=a^2\operatorname{Var}(X).</math>

The variance of a sum of two random variables is given by
<math display="block">\begin{align}
\operatorname{Var}(aX + bY) &= a^2\operatorname{Var}(X) + b^2\operatorname{Var}(Y) + 2ab\, \operatorname{Cov}(X,Y) \\[1ex]
\operatorname{Var}(aX - bY) &= a^2\operatorname{Var}(X) + b^2\operatorname{Var}(Y) - 2ab\, \operatorname{Cov}(X,Y)
\end{align}</math>

where <math>\operatorname{Cov}(X,Y)</math> is the [[covariance]].