IE143-SQ03 - University of the Philippines Diliman...

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University of the Philippines – Diliman Department of Industrial Engineering and Operations Research IE 143 Short Quiz Short Quiz 3 – Class 2 10 out of 10 All answers and relevant solutions should be written at the back of this questionnaire. 1. Which of the following are transition matrices? (1 point) A. g 0.5 0.3 0.2 0.1 0.75 0.15 1 0 0 G B. g 0.15 0.2 0.6 0.1 0.8 0.1 0.5 0.45 0.05 G C. g 0 1 0 0 0 1 1 0 0 G D. g 0.05 0.35 0.6 0.65 0.55 −0.2 0.1 0.01 0.89 G 2. True or False: A periodic class is also a recurrent class. (1 point) 3. Assume the following is a one-step transition probability matrix. ± ² ³ ± ² ³ g 0.1 0.2 0.7 0.3 0.4 0.3 0.2 0 0.8 G a. What is the probability of going from A to C in exactly one step? (1 point) b. What is the probability of going from C to B in exactly two steps? (2 points) c. Draw the transition probability graph for this Markov chain. (1 point) d. Identify which the states are recurrent. (1 point) e. Find the long-term probabilities of being in state A, B, or C in a given step. (3 points)
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IE143-SQ03 - University of the Philippines Diliman...

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