Hw6-ORIE3510_S12 - ORIE 3510 Homework 6 Instructor: Mark E....

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ORIE 3510 – Homework 6 Instructor: Mark E. Lewis due Wednesday March 9, 2012 (ORIE Hallway drop box) 1. One light bulb at Rhodes student lounge has a maximum life of m days. In each day, the bulb will go crashed with probability p , in which case a new bulb must be installed to replace the broken one. Also a bulb that has survived for m days must be replaced regardless of whether it is still working or not. In the long run, what is the fraction of time that a student will find a newly-installed fresh light bulb in the lounge? 2. Consider a discrete Markov chain with transition matrix P = 0 1 2 3 0 . 1 0 . 3 0 . 3 0 . 3 0 . 1 0 . 1 0 . 5 0 . 3 0 . 3 0 . 2 0 . 1 0 . 4 0 . 3 0 . 3 0 . 3 0 . 1 Suppose that the chain initially starts randomly with equal probabilities in one of the 4 states. (a) What is the probability that state 0 is visited before state 3? (b) What is the expected waiting time until state 0 is visited for the first time? (c) What is the expected time between two visits to state 0?
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This note was uploaded on 03/08/2012 for the course OR&IE 3510 taught by Professor Lewis during the Spring '10 term at Cornell University (Engineering School).

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Hw6-ORIE3510_S12 - ORIE 3510 Homework 6 Instructor: Mark E....

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