Calculate the variance

  • #1

Homework Statement


Find the variance of Y=3x^2+3x+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:

Answers and Replies

  • #2
haruspex
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Var(3x^2 +3z +1) = 9Var(x^2) +9Var(x)
I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?
 
  • #3
I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?

Oh. It assumes no covariance.
 
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  • #4
Ray Vickson
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Homework Statement


Find the variance of Y=3x^2+3x+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.

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

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