Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7,
7:15, 7:30, 7:45, and so on. Suppose that a passenger arrives at the stop at a time that is uniformly
distributed between 7 and 7:15.
(a) Let X be the number of minutes past 7 that the passenger arrives at the stop. Find the pdf of
X.
(b) Find the probability that a passenger waits less than 5 minutes for a bus.