Answer Happy

Engineering Probability Question
Problem 32 Customer arrivals at a store are Poisson with parameter 1 = 18 per hour. Each customer will in- stantly (with no delay) make a purchase with probability 1/3, independently of all other customers. (i) (2 pts.) If the store opens at 10:00AM, what is the expected time of the first customer arrival? (ii) (3 pts.) What is the expected time of the first purchase? (iii) (3 pts.) How likely is it that exactly six customers arrive between 10:00 AM–10:30AM, three of whom make a purchase? (iv) (4 pts.)) Suppose that over a time period of t hours, exactly nine customers arrive. What is the conditional probability that all of them arrived in the first half (t/2 hours) of that period? Does the answer depend on t? (v) (4 pts.) Suppose that over a time period of t hours, exactly nine customers arrive. What is the conditional probability that exactly four of these customers make a purchase? Does the answer depend on t? (vi) (4 pts.) Let X, be the number of purchases over a time period of two hours, and Y, be the number of arrivals in the first hour of that period). Determine E[X2Y1).