[4 6. Bonus. (not required) (You should read Section 10.1 before attempting part b) Random Irrigation Services provides irrigation of fields using a robotic sprinkler which moves to a random point P in the field and than irrigates a circle of radius 1 with center P randomly chosen within the field, and then repeats this a large number of times. Farmer Leopold Gauss hires this service to irrigate a narrow field of width 2m where m > 1 (you may assume it is infinitely long), bordered by a fence on either side. (See the Figure below). 2m a. Let A be the area of the region irrigated that lies outside the fences. (for example in the figure it is the area of the shaded region) Find E(A) and Var(A). b. Suppose the device repeats this process a total of 100 times, where the points P1, ..., Ploo are randomly chosen and independent of one another. Assume m = 2 and find the probability that more than 15% of the irrigated area falls outside the fences