1. When the 6 or 8 bus arrives at the university, the next bus arrives after Exp(1/4) time (units are in hours). (a) What is the expected number of buses that arrive in a two-hour period? [1 mark] (b) What is the probability that at least two buses arrives in a 10 minute period. [1] (c) Consider the 6 consecutive 10 minute periods between 3pm and 4pm. What is the probability that at least one of these periods has two or more buses arriving in it? [2] (d) I arrive at the bus stop and start my watch. What is the expected amount of time until the sixth bus arrives. What is the standard deviation of this time? [2] (e) Rush hour traffic limits the number of buses arriving. Given that exactly two buses arrive between 8:30am and 9:30am, what is the expected arrival time of the second bus? [3] (f) I want to get the number 6 bus. Each bus that arrives is a number 6 bus independently with probability 0.25. What is the expected amount of time to wait until a number 6 bus? [1]