3.23 Coverage; Robbins's theorem on random sets Imagine a square region of a city having unit area. Suppose that there are N ambulettes whose positions are independently and uniformly distributed over a region T consisting of all points in the city whose distance from the square is not greater than a. The area of T is 1 + 4a + a². A point in the unit square is said to have sufficient ambulance coverage if at least one ambulance is within a (Euclidean) distance a of the point. Find the expected area within the square which is sufficiently covered.