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Calculate the variance

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the variance of Y=3x^2+3x+3

    3. The attempt at a solution
    Let Y = 3x^2 +3x +3

    Var(Y) = Var(3x^2 +3x +3) = 9Var(x^2) +9Var(x) = 9 [E[X^4] - E[X^2]^2 +E[X^2] - E[X]^2]
    This is wrong.
    Last edited: Oct 26, 2014
  2. jcsd
  3. Oct 26, 2014 #2


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    I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?
  4. Oct 26, 2014 #3
    Oh. It assumes no covariance.
    Last edited: Oct 26, 2014
  5. Oct 26, 2014 #4

    Ray Vickson

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    You have assumed that ##\text{Cov}(X^2,X) = 0,## which is not generally true.
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