PROBLEM 2 Buses arrive at a certain stop according to a Poisson process with rate . if you take the bus from that stop then it takes a time R, measured from the time you enter the bus, to arrive home. If you walk from the bus stop then it takes a time W to arrive home. Your policy when arriving at the bus stop is to wait up to a time s, and if a bus has not arrived by that time then you walk home. Let L be the time from when you arrive at the bus stop until you reach home. 1) Express E[L] in terms of2, s, W and R (10 Pts) 2) Show that in order to minimizes EIL], s' should be efther 0 or o (5 Pts) Hint: Int I at (exp-fat)dt, (t, 0, bl]-[1-(exp-(ab)/a-b (exp-(ab) PROBLEM 2 Buses arrive at a certain stop according to a Poisson process with rate . if you take the bus from that stop then it takes a time R, measured from the time you enter the bus, to arrive home. If you walk from the bus stop then it takes a time W to arrive home. Your policy when arriving at the bus stop is to wait up to a time s, and if a bus has not arrived by that time then you walk home. Let L be the time from when you arrive at the bus stop until you reach home. 1) Express E[L] in terms of2, s, W and R (10 Pts) 2) Show that in order to minimizes EIL], s' should be efther 0 or o (5 Pts) Hint: Int I at (exp-fat)dt, (t, 0, bl]-[1-(exp-(ab)/a-b (exp-(ab)