Buses arrive at a bus station with i.i.d. interarrival times following an exponential distribution with intensity . Alice arrives at the bus station at a deterministic time t. a. (4pts) What is the expected waiting time for Alice until next bus comes? b. (6pts) Let be the time when the last bus arrived before time t. Show that t follows an exponential distribution with parameter . c. (6pts) Show that the expected interarrival time between the last bus which arrived before time t and the first bus which arrives after time t is 2 . Explain why it is different from the general expected interarrival time 1 .