A subway station carries both blue (B) line and red (R) line trains. Red line trains and blue line trains arrive as independent Poisson processes with rates λR = 0.15 and λB = 0.30 trains/min respectively. You arrive at the station at random time t and watch the trains for one hour.
(a) What is the PMF of N, the number of trains that you count passing through the station?
(b) Given that you see N = 30 trains, what is the conditional PMF of R, the number of red trains that you see?