exam210A - middle and rank C is the highest. Initially,...

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ISyE 3232 A Exam # 2 Spring 2010 Name Please be neat and show all your work so that I can give you partial credit. GOOD LUCK. Question 1 Question 2 Question 3 Question 4 Total 1
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(25) 1. A basketball player makes a shot with the following probabilities: 1/2 if he has missed the last two times 2/3 if he has hit one of his last two shots 3/4 if he has hit both of his last two shots Compute the long run probability that he makes a shot. 2
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(25) 2. Consider a bank with two tellers. Teller 1 has an exponential service time with mean 3 minutes and teller 2 has an exponential service time with mean 6 minutes. Alice, Betty, and Carol enter the bank at the same time. Alice goes to teller 1 and Betty goes to teller 2 while Carol waits for the first available teller. a. (10) What is the expected time that Carol spends in the bank? b. (10) What is the expected time until the last of the three customers leaves the bank? c. (5) What is the probability that Carol is the last one to leave? 3
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(25) 3. A firm has a three rank hierarchy: Rank A is the lowest, rank B is the
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Unformatted text preview: middle and rank C is the highest. Initially, there are 100 employees at rank A, 80 at rank B, and 60 at rank C. Let the economic value of an employee at ranks A, B and C be 1,2 and 3 respectively. Assume that there is no demotion and each employee advances through the ranks according to the following one year probability transition matrix P = . 4 0 . 4 0 . 1 0 . 1 . 0 0 . 5 0 . 4 0 . 1 . 0 0 . 0 0 . 8 0 . 2 . 0 0 . 0 0 . 0 1 . where X represents employees exit from the rm. What is the expected total economic value of the rm after 2 years? 4 (25) 4. Sue and Liz arrive at a beauty salon together and plan to leave together. Sue needs a perm, and Liz a manicure. The duration of a perm is exponentially distributed with rate 5 /hr ; that of a manicure is exponentially distributed with rate 10 /hr . If both are served immediately, what is expected duration one has to wait for the other? 5...
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exam210A - middle and rank C is the highest. Initially,...

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