Buses arrive at the station randomly and independently, at a rate of 1 per five minutes; the number that arrive in t minutes is thus a Poisson random variable B with = 0.2t. (a) Calculate the probability that exactly two buses come in a 10 minute interval. (b) How much time should you allow so that there is a 0.99 probability that at least one bus will arrive? (c) Suppose that, over a 10 minute interval, one bus arrives during the first x minutes and a second bus arrives during the remaining time. Calculate the probability of this event as a function of x; x does not have to be a whole number. Compare your result with the answer to (a); how and why do the differ?