Question

Ex. 10

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 Yare 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 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|≤ 16}.]

Answer 1

b)P(both arrive between 5:18 and 5;37) =(19/60)*(19/60)=0.100

c)P(have dinner ) =1-P(both does not have dinner )=1-(50/60)*(50/60) =0.306