Consider Markov chain with states (1, 2, 3, 4) and suppose that transitions happen once a day. Tran- sition matrix P is given by Note that p4= p² = P = 0.2 0 0.7 1 0.51 0.08 0.3 0.12) 0.73 0.18 0.09 0.09 0.31 0.23 0.26 0.31 0.2 0.3 0.1 0.4 /0.4355 0.1602 0.2502 0.2094 0.5496 0.1385 0.2676 0.1677 0.4686 0.219 0.2123 0.2625 0.432 0.213 0.153 0.242 0.3 0.1 0.4 0 0.9 0.1 0.2 0.1 0 0 0 0 , p3 . = , P = 0.432 0.213 0.153 0.242) 0.299 0.237 0.244 0.319 0.554 0.145 0.264 0.173 0.51 0.08 0.3 0.12 /0.47164 0.18069 0.21275 0.21524 0.46494 0.2184 0.20637 0.26045 0.50483 0.18304 0.26519 0.23057 0.4355 0.1602 0.2502 0.2094 i. Suppose that on Monday the system was observed to be in state 1, what is the probability that it will be in state 4 on Wednesday? ii. Suppose that on Monday the system was observed to be in state 1 and on Tuesday in state 2. What is the probability that it will be in state 3 on Friday? iii. Suppose that on Monday the system was observed to be in state 1, what is the probability that it will stay in that state until Friday? iv. Suppose that on Monday the system has 60% chance of being in state 1 and 40% chance of being in state 2. What is the probability that it will be in state 3 on Wednesday?

Consider Markov chain with states (1, 2, 3, 4) and suppose that transitions happen once a day. Tran- sition matrix P is given by Note that p4= p² = P = 0.2 0 0.7 1 0.51 0.08 0.3 0.12) 0.73 0.18 0.09 0.09 0.31 0.23 0.26 0.31 0.2 0.3 0.1 0.4 /0.4355 0.1602 0.2502 0.2094 0.5496 0.1385 0.2676 0.1677 0.4686 0.219 0.2123 0.2625 0.432 0.213 0.153 0.242 0.3 0.1 0.4 0 0.9 0.1 0.2 0.1 0 0 0 0 , p3 . = , P = 0.432 0.213 0.153 0.242) 0.299 0.237 0.244 0.319 0.554 0.145 0.264 0.173 0.51 0.08 0.3 0.12 /0.47164 0.18069 0.21275 0.21524 0.46494 0.2184 0.20637 0.26045 0.50483 0.18304 0.26519 0.23057 0.4355 0.1602 0.2502 0.2094 i. Suppose that on Monday the system was observed to be in state 1, what is the probability that it will be in state 4 on Wednesday? ii. Suppose that on Monday the system was observed to be in state 1 and on Tuesday in state 2. What is the probability that it will be in state 3 on Friday? iii. Suppose that on Monday the system was observed to be in state 1, what is the probability that it will stay in that state until Friday? iv. Suppose that on Monday the system has 60% chance of being in state 1 and 40% chance of being in state 2. What is the probability that it will be in state 3 on Wednesday?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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