Buses arrive at a station according to a Poisson process with rate 2 per hour. Passengers arrive at the station according to another independent Poisson process with rate 4 per hour. All the passengers will wait until a bus arrives. Each arrival bus picks up all the waiting passengers and leaves immediately. Start from 0pm.

(a) Find the expected number of buses that arrive between 1pm and 3pm.

(b) Find the probability that the second passenger arrives between 1pm and 3pm.

(c) Find the variance of the number of passengers taken away by the third bus.

(d) Find the probability that the first two passengers are taken away by the second bus