Originally Posted by

**Moo** Hello,

(by the way, you wrote $\displaystyle U_2^2$ instead of $\displaystyle U_1^2$)

And in order to do this problem, you have to assume that the three rv's are independent.

Your integral is that of $\displaystyle E[U_1^2-4U_2U_3]$ so this is not what you want.

In order to find the probability you're looking for, you need to integrate the joint pdf of the three rv's over the region where $\displaystyle u_1^2-4u_2u_3>0$

So this gives $\displaystyle \displaystyle \int_0^1 \int_0^1 \int_0^1 \bold{1}_{\{u_1^2-4u_2u_3>0\}} du_3 du_2 du_1$

So this gives you a new boundary for the integral with respect to $\displaystyle u_3$... continue and you will find the answer