A surveyor wishes to lay out a square region with each side

A surveyor wishes to lay out a square region with each side having length L. However, because of measurement error, he instead lays out a rectangle in which the north-south sides both have length X and the east-west sides both have length Y. Suppose that X andY are independent and that each is uniformly distributed on the interval [L A, L + A] (where 0 < A < L). What is the expected area of the resulting rectangle?
E(area) =  

Solution