During rush hours at the Paris metro station, trains arrive according to the Poisson distribution with expected number of ten trains per 60 minute period.
(a) Determine the probability mass function of train arrivals in a period of length t minutes?
(b) Determine the probability that two trains will arrive in a three minute period?
(c) Explain the probability that no trains will arrive in a ten minute period?
(d) Find out the probability that at least one train will arrive in the period of length t minutes and employ this to calculate how long is required to be 95% sure that a train will arrive?