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 5 Annie’s arrival time and Y 5 Alvie’s arrivaltime. Suppose X and Y are independent with each uniformlydistributed on the interval [5, 6].a. What is the joint pdf of X and Y?b. What is the probability that they both arrive between5:15 and 5:45?c. If the first one to arrive will wait only 10 min beforeleaving to eat elsewhere, what is the probability thatthey have dinner at the health-food restaurant? [Hint:The event of interest is A5{(x, y): u x2y u # 1y6}.]

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