Consider the Markov chain on {1, 2, 3} with transition matrix
P =
- a. Show that P is a regular matrix.
- b. Find the steady-state
vector for this Markov chain. - c. What fraction of the time does this chain spend in state 2? Explain your answer.
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Linear Algebra and Its Applications (5th Edition)
- 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)arrow_forwardExplain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.arrow_forwardConsider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show that the steady state matrix X depends on the initial state matrix X0 by finding X for each X0. X0=[0.250.250.250.25] b X0=[0.250.250.400.10] Example 7 Finding Steady State Matrices of Absorbing Markov Chains Find the steady state matrix X of each absorbing Markov chain with matrix of transition probabilities P. b.P=[0.500.200.210.300.100.400.200.11]arrow_forward
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