I need to solve this probelm and will greatly appretiate help.
I need to amximize this above function with respect to X, where Y is a uniformly distributed variable between -0.5 and 0.5. X is dependent somehow on Y. Z is another variable not important since the solution to this problem should be .
I know that this solution will be dependen somehow on the probability distribution of Y, but I do not kow how to obtain the F.O.C. and how to differentiate the integral (the expectation of this function).
The more detailed help the better!