1.(22pts) A bus stop is served by only two bus lines that operate independently. Onaverage Line A buses arrive every 15 minutes, and Line B buses arrive every 20 minutes.We model the passage times of both bus lines as Poisson processes. Assume that a pas-senger will always take the first bus that arrives at the stop.(a) (4pts) Give the rate parametersλ1andλ2in the two Poisson processes (with the unit“per hour”).
(b) (4pts) If Alice is waiting for Line A and she can only take a Line A bus to her desti-nation, what is the probability that she has to wait for more than 15 minutes?