Maria arrives at a bus stop at a uniformly random time. When Maria arrives at the bus stop, either of two independent bus lines (both of which can take her home) may come by. Company A’s bus arrival times are exactly 10 minutes apart, whereas the time from one Company B bus to the next is distributed as Expo( 1/10) . What is the probability that Company B’s bus arrives first? What is the PDF of Maria’s waiting time for a bus? Be sure to state what the support of the distribution is. Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct.