Customers arrive at a restaurant as a nonhomogeneous Poisson process having the intensity function 0

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Customers Arrive At A Restaurant As A Nonhomogeneous Poisson Process Having The Intensity Function 0 T 4 T Fi 1 (99.11 KiB) Viewed 21 times

Customers arrive at a restaurant as a nonhomogeneous Poisson process having the intensity function 0 <t < 4; \(t) = fi = 4, 4<t < 5; 5 – (t/5), 5<t < 10, where t is measured in hours from 8:00 am. 12:30 pm. i. Find the probability that no customer arrives during the hours 11:00 am to [3 marks] ii. Find the expectation of the number of customers that arrive during the hours 8:00 am to 5:00 pm. [3 marks] iii. Suppose that there is one customer arriving at 8:30 am. What is the prob- ability that the next customer arrives before 9:00 am? [3 marks] iv. Given that 4 customers have arrived during the hour 12:00 noon to 1:00 pm, what is the probability that 2 customers arrived in the first 30 minutes? [3 marks]