Assignment:
Annie and Alvie have agreed to meet between 5:00 pm and 6:00 pm 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 10 minutes 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 | ≤ 1/6}.]
Provide complete and step by step solution for the question and show calculations and use formulas.