3. A store opens at 9 am and closes at 6pm on a day. From 9 am until 11 am customers arrive at a Poisson rate of 4 per h

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3 A Store Opens At 9 Am And Closes At 6pm On A Day From 9 Am Until 11 Am Customers Arrive At A Poisson Rate Of 4 Per H 1 (136.57 KiB) Viewed 34 times

3. A store opens at 9 am and closes at 6pm on a day. From 9 am until 11 am customers arrive at a Poisson rate of 4 per hour. Between 11 am and 1pm they arrive at a Poisson rate of 8 per hour. From 1 pm to 3pm the arrival rate increases steadily from 8 per hour at 1pm to 10 per hour at 3pm; and from 3 pm to 6pm the arrival rate drops steadily from 10 per hour at 3pm to 4 per hour at 6pm. (a) Determine the intensity function of the number of customers that enter the store on a given day. (5 marks] (b) What is the probability that no customers arrive from 9 : 30 am to 11:30 am on a given day? [5 marks] : (c) What is the expected number of arrivals from 3 : 30 pm to 5 : 30 pm on a given day? [5 marks] (d) What is the probability of observing exactly 3 customers from 2 pm to 4pm on a given day? (This probability is small, please use scientific notations.) [5 marks]