Problem 1: Busses arrive at the NERS bus stop with an inter-arrival time that is exponentially distributed with parameter =5 busses per hour. This also means that the number of busses to arrive in an hour follows a Poisson distribution with an arrival rate of =5 busses per hour. This also means that the average headway (time between bus arrivals) is 12 minutes. a) Find the probability that the time between successive bus arrivals is less than or equal to 20 minutes or 1/3 of an hour. b) Find the probability that the time between successive bus arrivals exceeds 20 minutes. c) Find the probability that there will be exactly 6 bus arrivals in a two-hour period. d) Find the probability that there will be 6 or fewer bus arrivals in a two-hour period. e) Find the probability that there will be more than 6 bus arrivals in a two-hour period. f) You arrive at the bus stop and see that your friend Lindsey is there as well. You ask her how long she has been waiting for the bus. She says that she has been there for 10 minutes already. Given that she has been there for 10 minutes or 1/6th of an hour, what is the conditional additional time that you expect to wait until the next bus arrives