(c) Suppose that each customer will, with probability 0.85, not buy rice or, with probability 0.15, buy a bag of rice. E

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C Suppose That Each Customer Will With Probability 0 85 Not Buy Rice Or With Probability 0 15 Buy A Bag Of Rice E 1 (90.02 KiB) Viewed 23 times

(c) Suppose that each customer will, with probability 0.85, not buy rice or, with probability 0.15, buy a bag of rice. Each customer acts independently. For simplicity, assume that the purchase of rice is done at the time the customer arrives at the supermarket. Suppose that there are only 3 bags of rice in the supermarket at the current moment. i. What is the expected time until all bags of rice are sold? (4 marks] ii. Suppose that rice will be restocked at time T, where T follows the exponential distribution with mean 2. What is the probability that the restock happens before the fourth customer who wants to buy rice arrives? (Hint: note that [****e xk-1e-Bx dx = (k – 1)! Bk for B > 0 and positive integer k.) [6 marks]