Starting from time 0, buses arrive at a specic stop according to a Poisson process with rate lambda. Passengers arrive at the stop according to an independent Poisson Process of rate u. When a bus arrives, all waiting customers instantly enter the bus and subsequent customers wait for the next bus.

(a) Find the probability mass function for the number of customers entering a bus.(

b) Given that a bus arrives at 10:30 PM and no bus arrives between 10:30 and 11, and the probability mass function for the number of customers on the next bus.