A bus arrives at a bus stop at a uniformly distributed time over the interval 0 to 1
Chapter 5, Problem 5.68(choose chapter or problem)
A bus arrives at a bus stop at a uniformly distributed time over the interval 0 to 1 hour. A passenger also arrives at the bus stop at a uniformly distributed time over the interval 0 to 1 hour. Assume that the arrival times of the bus and passenger are independent of one another and that the passenger will wait for up to 1/4 hour for the bus to arrive. What is the probability that the passenger will catch the bus? [Hint: Let Y1 denote the bus arrival time and Y2 the passenger arrival time; determine the joint density of Y1 and Y2 and find P(Y2 Y1 Y2 + 1/4).]
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