Suppose that at a subway station, the arrival rate starts at 1 at 5:00 AM. It increases to 4 at 7:00 AM, increases to 6 at 8:30 AM, and decreases to 3 at 10:30 AM until noon, which is the time when first shift employees leave work, also consider that the arrival rate is constant between these points.

a) What is the distribution of the number of arrivals on the day (From 5 to 12)?

b) What is the probability that no one arrives before 8:00 AM?