Calculating Variance for Y=3x^2+3x+3

[hellokitten]

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.

 

[haruspex]

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?

 

[hellokitten]

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.

 

[Ray Vickson]

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.