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Basically I want to know how to extend the following formula to the three variable case:

$$\mbox{var}(aX+bY) = a^2\mbox{var}(X)+ b^2\mbox{var}(Y) + 2ab \sqrt{ \mbox{var}(X) \mbox{var}(Y)} \mbox{corr}(X,Y)$$

How can I calculate $\mbox{var}(aX + bY + cZ) $?

The answer to the two variable case is explained here. It's possible that the general case is covered too, but I didn't quite follow the matrix algebra and wondered if there is an explicit solution for the three variable case.

Community
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Yugmorf
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    The answer is here: [Determining variance from sum of two random correlated variables](http://math.stackexchange.com/q/115518/29951). –  Nov 20 '12 at 15:51

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The variance of the sum of three variables is given by

$Var(aX+bY+cZ) = a^2Var(X) + b^2Var(Y) + c^2Var(Z) + 2abCov(X,Y) + 2acCov(X,Z) + 2bcCov(Y,Z)$

JorgeT
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