# Calculate the variance

Tags:
1. Oct 26, 2014

### hellokitten

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. Oct 26, 2014

### haruspex

I guess the z should be X, or 9var(x) should be 9Var(Z). Either way, what assumption does that step require?

3. Oct 26, 2014

### hellokitten

Oh. It assumes no covariance.

Last edited: Oct 26, 2014
4. Oct 26, 2014

### Ray Vickson

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