Calculate the Variance of a Linear Combination

[tnqz44]

Homework Statement

I want to calculate the variance of a linear combination (b1, b2, b3, b4, b5, b6). I know what the variance equation is but I'm not sure if I have expanded it right.

Homework Equations

http://en.wikipedia.org/wiki/Variance

The Attempt at a Solution

Var(b1, b2, b3, b4, b5, b6) = Var(b1)^2 + Var(b2)^2 + Var(b3)^2 + Var(b4)^2 + Var(b5)^2 + Var(b6)^2 + 2Cov(b1,b2) + 2Cov(b1,b3) + 2Cov(b1,b4)+ 2Cov(b1,b5) + 2Cov(b1,b6) + 2Cov(b2,b3)+ 2Cov(b2,b4) + 2Cov(b2,b5) + 2Cov(b2,b6) + 2Cov(b3,b4)+ 2Cov(b3,b5) + 2Cov(b3,b6) + 2Cov(b4,b5) + 2Cov(b4,b6) + 2Cov(b5,b6)
Please tell me if I got it correct, very much appreciated :)

 

[rootX]

Yes, it looks correct. Wolfram has neater version IMO
http://mathworld.wolfram.com/Variance.html

 

[Ray Vickson]

Homework Statement

I want to calculate the variance of a linear combination (b1, b2, b3, b4, b5, b6). I know what the variance equation is but I'm not sure if I have expanded it right.

Homework Equations

http://en.wikipedia.org/wiki/Variance

The Attempt at a Solution

Var(b1, b2, b3, b4, b5, b6) = Var(b1)^2 + Var(b2)^2 + Var(b3)^2 + Var(b4)^2 + Var(b5)^2 + Var(b6)^2 + 2Cov(b1,b2) + 2Cov(b1,b3) + 2Cov(b1,b4)+ 2Cov(b1,b5) + 2Cov(b1,b6) + 2Cov(b2,b3)+ 2Cov(b2,b4) + 2Cov(b2,b5) + 2Cov(b2,b6) + 2Cov(b3,b4)+ 2Cov(b3,b5) + 2Cov(b3,b6) + 2Cov(b4,b5) + 2Cov(b4,b6) + 2Cov(b5,b6)


Please tell me if I got it correct, very much appreciated :)

By Var(b1,b2,b3,b4,b5) do you mean Var(b1+b2+b3+b4+b5)? If so, why not write it properly?

Anyway, if you do mean Var(b1+b2+b3+b4+b5), then your formula is WRONG. I don't want to say more, because that would be giving the solution, but I will just say: go back and read what the formula in your link says, then look *very carefully* at what you have written. Can you see the difference?

RGV