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Unformatted text preview: OR Models Practice Exam #2 Fall Semester 2011 Name: No books, notes or calculators are allowed in this exam. 1. (35 pts) Three particles are divided between two cells, cell #1 and cell #2. A cell may contain 0, 1, 2, or 3 particles. During each period, one of the three particles is chosen at random and moved to the other cell. (a) (15 pts) Formulate this problem as a discrete-time Markov chain, i.e., (i) clearly define the states, (ii) give the state-transition diagram, and (iii) give the one-step transition matrix. (b) (10 pts) Suppose we seek the long-run fraction of time that cell #1 contains 0, 1, 2, and 3 particles, respectively. Write down a system of equations whose solution gives these values. (You do not need to solve the system of equations.) (c) (10 pts) Suppose cell #1 currently contains no particles and we seek the average number of periods that will go by before it contains 2 particles. Write down a system of equations whose solution will give this value. Clearly specify which variable’s value will give the desired answer.solution will give this value....
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This note was uploaded on 12/19/2011 for the course M E 366l taught by Professor Staff during the Fall '08 term at University of Texas at Austin.
- Fall '08