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.