Annie and Alivie have agreed to meet between 5-00p. m. and 6-00p. 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?b) What is the probability that they both arrive between 5-15 and 5-45?c) If the first one to arrive will wait 10 min before leavingto 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| <= 1/6}.)