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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 discretetime Markov chain, i.e., (i) clearly define the states, (ii) give the statetransition diagram, and (iii) give the onestep transition matrix. (b) (10 pts) Suppose we seek the longrun 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
 Staff

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