Siegbert runs a hot dog stand that opens at 8 A.M. From 8 until 11 A.M. customers seem to arrive, on the average, at a s

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Siegbert runs a hot dog stand that opens at
8 A.M. From 8 until 11 A.M. customers seem to
arrive, on the average, at a steadily increasing rate that starts
with an initial rate of 5 customers per hour at
8 A.M. and reaches a maximum of 20 customers per hour at
11 A.M. From 11 A.M. until 1 P.M. the
(average) rate seems to remain constant at 20 customers per hour.
However, the (average) arrival rate then drops steadily from
1 P.M. until closing time at 5 P.M. at which
time it has the value of 12 customers per hour. If we assume that
the numbers of customers arriving at Siegbert’s stand during
disjoint time periods are independent, then what is a good
probability model for the preceding? What is the probability that
no customers arrive between 8:30 A.M. and
9:30 A.M. on Monday morning? What is the expected number
of arrivals in this period?