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Unformatted text preview: ORIE 361 – Preliminary Examination Spring 2008 Instructor: Mark E. Lewis March 4, 2008 This is a closed book, closed notes exam. However, you are only allowed to use a single 8.5 X 11 inch sheet of paper with whatever formulas or notes you deem appropriate. No other re sources are allowed . Please note that communication devices are NOT allowed in sight during the exam. You have 90 minutes to complete the exam. The total possible number of points is 100 with a 2 point bonus question. The completed exam must be turned in to me or the TA by the end of the exam period on the day of the exam. NO EXCEPTIONS . The academic integrity code is to be adhered to at all times. Good luck! Name: Section: netid: Other than that given by the instructor or proctors, I have not been given nor received aid on this exam. Signature: 1 ORIE 361 – Spring 2008, Prelim 2 This is the answer sheet for all of your questions. Be certain to transcribe all of your answers to this sheet as this is the only sheet from which your answers will be considered. 1. (a) The expectation = (b) Answer (yes or no): (c) The limit = (d) Answer (yes or no): 2. (a) Answer (yes or no): (b) Answer (yes or no): (c) Expression for W j‘ : 3. Circle (only) one. (a) True False (b) True False (c) True False (d) True False (e) True False (f) True False 4. (a) Answer: (b) Answer: (c) i. Answer: ii. Answer: ORIE 361 – Spring 2008, Prelim 3 iii. Answer: iv. Answer: v. Answer: vi. Answer: vii. Answer: 5. (a) i. The state space S = ii. Transition matrix: P = . iii. Conditions under which all states are Positive recurrent: Null recurrent: Transient: iv. The long run average cost: (b) (the finite capacity case) i. S = ORIE 361 – Spring 2008, Prelim 4 ii. Transition matrix: P = . iii. Answer: Bonus question answer: ORIE 361 – Spring 2008, Prelim 5 1. (Costs) { 12 points } Consider a Markov chain on state space S = { 1 , 2 } with one step transition matrix as defined below...
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 Spring '07
 LEWIS,M.
 Markov chain, discretetime Markov chain

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