B For the Markov process with transition diagram shown at right, say why you would expect the steady state to have equal probabilities for the four states A, B,C, D, no matter what the probabilities r, s and t happen to be. [As is the normal convention, missing arrows all represent transitions with probability zero.]

Elementary Linear Algebra (MindTap Course List)
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Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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uestion 4*
B
For the Markov process with transition diagram shown
at right, say why you would expect the steady state to
have equal probabilities for the four states A, B,C, D,
no matter what the probabilities r, s and t happen to
be. [As is the normal convention, missing arrows all
represent transitions with probability zero.]
Write out the transition
matrix T for this process:
Use T" to confirm the steady state vector implied by part (a).
For r= 0.2, s= 0.5 and t= 0.3 how many time steps are needed to arrive at the
steady state, to 2 decimal places accuracy, starting from any initial state vector?
[Hint: Use a matrix calculator to take powers of T" as in Q2(a).]
Transcribed Image Text:uestion 4* B For the Markov process with transition diagram shown at right, say why you would expect the steady state to have equal probabilities for the four states A, B,C, D, no matter what the probabilities r, s and t happen to be. [As is the normal convention, missing arrows all represent transitions with probability zero.] Write out the transition matrix T for this process: Use T" to confirm the steady state vector implied by part (a). For r= 0.2, s= 0.5 and t= 0.3 how many time steps are needed to arrive at the steady state, to 2 decimal places accuracy, starting from any initial state vector? [Hint: Use a matrix calculator to take powers of T" as in Q2(a).]
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