Originally Posted by

**notgoodatmath** Hi,

I'm stuck on the domain of integration change in the following problem:

I have a Uniform distribution, U(a,b).

I'm deriving the variance:

var = $\displaystyle \int^b_a \left(x-\frac{b+a}{2}\right)^2 \frac{1}{b-a} dx$

Use a change of variable substitution: $\displaystyle y =x - \frac{b+a}{2}$

Take the constant out

$\displaystyle var = \frac{1}{b-a} \int^\frac{b-a}{2}_{-\frac{b-a}{2}} y^2 dy$

I'm not sure why the domain of integration has changed from a to b, to $\displaystyle \frac{b-a}{2}$. I'm presuming it's to do with the y change of variable. Any ideas?