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Calculate the Variance of a Linear Combination

  1. Apr 23, 2012 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

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

    3. 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 :)
     
  2. jcsd
  3. Apr 23, 2012 #2
  4. Apr 23, 2012 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    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
     
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