Poisson

A store opens from 8am to 5pm. From 8am until 10am, customers arrive according to a Poisson process with rate 4 per hour. Between 10am and 12pm they arrive at a Poisson rate of 8 an hour. From 12pm to 2pm, the arrival rate increases steadily from 8 per hour at 12pm to 10 per hour at 2pm; and from 2pm to 5pm the arrival rate drop steadily from 10 per hour at 2pm to 4 per hour at 5pm. (a) Find a probability model for the number of the customers that enter the store in a given day. (b) Find the probability that at least 2 customers arrive at the store during 11am to 1pm. (0) Suppose that this store receives a benet $10 on average with a standard deviation $2 from each customer that enters to the store. Find the average benet of this store in a given day, together with its standard deviation. For a. day, the arrival rate can be written as 0, 0gt