WIR Math 166-copyright Joe Kahlig, 10A Page 1Week in Review # 10Section M.2: Regular Markov Processes• Regular Transition Matrix• Steady State Distribution• Limiting Matrix1. Determine which of these matrices are regular.(a)0 0.7 00.8 0 00.2 0.3 1(b)0 0.7 00.8 0 10.2 0.3 02. Find the steady state distribution.T =ABA B0.4 0.20.6 0.83. Find the steady state distribution.T =ABCA B C0 0.7 00.8 0 10.2 0.3 0Section M.3: Absorbing Markov Process• Absorbing State• Absorbing stochastic matrix• Limiting Matrix• Fundamental matrix4. Does the transition diagram have an absorbing state? Does it represent an absorbingMarkov process?BADC0.70.50.50.10.210.20.8WIR Math 166-copyright Joe Kahlig, 10A Page 25. Does the transition diagram have an absorbing state? Does it represent an absorbingMarkov process?BADC0.70.40.50.10.310.20.86. Does the transition matrix represent an absorbing Markov process(a) T =ABCDA B C D0.4 0 0.7 00 1 0 00.6 0 0.3 00 0 0 1(b) T =ABCDA B C D0.1 0 0.6 00.3 1 0.1 00.6 0 0.3 00 0 0 17. Find the limiting Matrix.ABCDA B C D0.1 0 0.5 00.3 1 0.1 00.4 0 0.3 00.2 0 0.1 1WIR Math 166-copyright Joe Kahlig, 10A Page 38. Use the transition matrix to answer the following.ABCDEA B C D E1 0 0 0.1 0.10 1 0 0.2 00 0 1 0.1 0.10 0 0 0.4 0.50 0 0 0.2 0.3(a) Find the limiting Matrix.(b) What is the probability that if you start in state D you will end up in state B?(c) What is the probability that if you start in state E you will end up in state C?(d) Find the fundamental matrix.(e) What is the expected number of iterations of the Markov process if you start inState D?(f) If you start in state E, what is the expected number of times that you would bein state D before entering an absorbing state?WIR Math 166-copyright Joe Kahlig, 10A Page 49. A mouse is placed in one of the compartments of the maze. The mouse takes twominutes to randomly select a door and then leaves the compartment. If the mouseenters another compartment, the procedure is repeated. The exit doors of the mazeare one-way and thus once a mouse leaves the maze it can not return.ABCExitExit(a) Find the transition matrix and the limiting matrix.(b) If the mouse starts in room A, what percent of the time will it exit the door inroom C?(c) Find the fundamental matrix.(d) If the mouse begins in room A, what is the expected amount of time it will spendin the maze?(e) If the mouse begins in room A, what is the expected amount of time it will spendin room B?(f) If the mouse begins in room B, what is the expected amount of time it will spendin room
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