(i) Define a Poisson process [2] A bus route in a large town has one bus scheduled every 15 minutes. Traffic conditions in the town are such that the arrival times of buses at a particular bus stop may be assumed to follow a Poisson process. Mr Bean arrives at the bus stop at 12 midday to find no bus at the stop. He intends to get on the firs: bus to arrive. (ii) Determine the probability that the first bus will not have arrived by 1.00 pm the same day. The first bus arrived at 1.10 pm but was full, so Mr Bean was unable to beard it. (iii) Explain how much longer Mr Bean can expect to wail for the second bus to arrive. (iv) Calculate the probability that at least two more buses will arrive between 1.10 pm and 1.20 pm. [2] [1] [2] [Total 7]