My question is a follow up to this: Expected value of maximum of two random variables from uniform distribution
(Another method than the one proposed by the chosen answer is to square the c.d.f. of a single uniform (which is the c.d.f. of the maximum). Then taking the derivative to get the p.d.f. of the maximum. Then finding the expected value.)
Consider U(0,V), and lets shift down the density downwards (from the original 1/V) in the interval [0, U], and to balance it out, shift the density upwards (from the original 1) in the interval [U, V] - call this new discontinuous random variable $D$.
Now I realize two values in $D$ and I want to find the expected value of the max. However, without indicator variables (don't know how to deal with those in calculus operations), I can't come up with a closed-form c.d.f. or survival function.