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The varience - stats

Why is Var(aX + bY) sometimes = a^2Var(X) + b^2Var(Y) but sometimes it's = aVar(X) + bVar(Y)
Original post by FusionNetworks
Why is Var(aX + bY) sometimes = a^2Var(X) + b^2Var(Y) but sometimes it's = aVar(X) + bVar(Y)


I don't think it's ever the second one.

Var(aX+bY)=a2Var(X)+b2Var(Y)+2abCov(X,Y)Var(aX + bY) = a^2 Var(X) + b^2 Var(Y) + 2abCov(X,Y)
With 2abCov(X,Y)=02abCov(X,Y)=0 if the variables are independent.

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