Expected Value Question

[Yobz]

What would be the expected value of X^2 on a uniform distribution between A and B?

In other words,
E(X) = (a+b)/2, what about E(X^2)?

[gaming_mouse]

[ QUOTE ]
What would be the expected value of X^2 on a uniform distribution between A and B?

In other words,
E(X) = (a+b)/2, what about E(X^2)?

[/ QUOTE ]

The integral from a to b of (X^2/(b-a)), or

(1/(b-a))*(1/3)*(b^3 - a^3)

[Yobz]

Cool, thanks for the quick reply. I just realized I could also do variance(x) = e(x^2)-e(x)^2 and var(x) = (b-a)^2/12 and e(x) is just (b+a)/2
and then I got (a^2+ab+b^2)/2, which is the same formula you gave