Romeo and Juliet have a dinner date at 7:00pm. Each person will arrive at the restaurant with a delay uniformly distributed between zero and one hour, independent of the other person. (a) What is the probability that the first person to arrive will end up waiting longer than 15 minutes for the other person? (b) Suppose that Romeo is impatient and will leave immediately if he does not see Juliet when he arrives. Juliet, on the other hand, is willing to wait 20 minutes for Romeo before calling it quits. What is the probability that they will have a date? (c) Now suppose that the restaurant, will cancel their reservation if neither person arrives by 7:30pm. What is the probability that Romeo and Juliet will have dinner? (d) Finally, suppose that Romeo and Juliet may independently chicken out of their date with probability 1/4. If they do not chicken out, then the delay is now exponentially distributed with rate A = 2/hour, independent of the other. Knowing that the other person might bail, both Romeo and Juliet will only wait 15 minutes before leaving. What is the probability that they meet? Note: the delay is no longer bounded between zero and one hour