I don't find this formula anywhere. Wikipedia has the case where:

Var(aX+bY)=a^2*Var(X)+a^2*Var(Y)+2abCov(X,Y).

How to derive formula for my case?

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- Jan 5th 2009, 07:27 AMtotalnewbieVariance(U) formula if U=aX+bY+cZ+d
I don't find this formula anywhere. Wikipedia has the case where:

Var(aX+bY)=a^2*Var(X)+a^2*Var(Y)+2abCov(X,Y).

How to derive formula for my case? - Jan 5th 2009, 09:06 AMLast_Singularity
So you want to find

Denote

Your problem then becomes

Of course, from the formula given on wikipedia, you know how to expand:

At this point, you can further simplify the first two variance terms. But for the last one, you need to know that

Can you finish the expansion from here?