3. Romeo and Juliet have a date, and each will arrive at the University Center at a time between noon and 1:00 PM. Let X be Romeo's arrival time and Y be Julieť's. Suppose X and Y are independent and both follow a uniform distribution between 0 and 1 hour. (a) Find the joint PDF of X and Y. (b) What is the probability that they both arrive between 12:15 PM and 12:45 PM? (c) If the first to arrive will wait for a maximum of 15 minutes and will leave if the other does not show up, what is the probability that they will meet?

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