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?
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 20 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| ≤ 1/3] (round your answer to three decimal places.)