Annie and Alvie have agreed to meet between 5:00 P. M. and 6:00 P. M. for dinner at a local health-food restaurant. Let X = Annie's arrival time and Y = Alvie's arrival time. Suppose X and Y are independent with each uniformly distributed on the interval [5, 6]. (a) What is the joint pdf of X and Y? f(x, y) = . 5 ≤ x ≤ 6, 5 ≤ y ≤ 6 (b) What is the probability that they both arrive between 5:15 and 5:45? (c) If the first one to arrive will wait only 5 min before leaving to eat elsewhere, what is the probability that they have dinner at the health-food restaurant? [Hint: The event of interest is A = (x, y): |x − y| ≤ 1/12 . ] (Round your answer to three decimal places.)