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5. Customers arrive according to a Poisson process of rate 30 per hour. Each customer is served and leaves

immediately upon arrival. There are two kinds of service, and a customer pays $5 for Service A or $15 for Service B. Customers independently select Service A with probability 1/3 and Service B with probability 2/3.

(a) What is the distribution of the number of customers who select Service A during the period 9:00am to 9:10am? (Give its name and any parameter(s).)

(b) During the period 9:30-10:30am, there were 32 customers in total. What is the probability that none of them arrived during 10:25-10:30am?

(c) What is the probability that the first two customers after 9:00am request Service B? 

(d) Determine the expected amount paid by all customers during a 10 minute period. 


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