78. A store opens at 8 a.m. From 8 until 10 a.m. customers arrive at a Poisson rate of four an hour. Between 10 a.m. and 12 p.m. they arrive at a Poisson rate of eight an hour. From 12 p.m. to 2 p.m. the arrival rate increases steadily from eight per hour at 12 p.m. to ten per hour at 2 p.m.; and from 2 to 5 p.m. the arrival rate drops steadily from ten per hour at 2 p.m. to four per hour at 5 p.m.

Determine the probability distribution of the number of customers that enter the store on a given day.