11. A commuter catches a bus each morning for 100 days. The buses arrive at the stop according to a Poisson process, at an average rate of one per 15 minutes, so if X.- is the waiting time on day 2', then X1- has an exponential distribution with parameter A = 1/15, i.e. E[Xi] : l/A, var[X'] : l/AZ. (a) Calculate the approximate probability that the total time the commuter spends waiting for buses over the 100 days exceeds 27 hours. (b) At the end of the 100 days the bus frequency is increased, so that buses arrive at one per 10 minutes on average. The commuter then catches a bus each day for a further 99 days. i. What is the approximate distribution of the total time the commuter spends waiting for buses over the extra 99 days. ii. Calculate the approximate probability that the total time spent waiting over the whole 199 days exceeds 40 hours