Question

I've already made the Markov matrix for this question, but I'm not sure how to do the second or third parts. I raised the Markov matrix to the sixth power in an attempt to do part 2, but I'm not sure how to account for node 3 being the starting point.

Consider the graph below with the edges labeled by the probability of a given transition and assume it represents a Markov model 2.1. Generate the Markov matrix. (+15 points) 0.67 1 2.3. Compute the probability of being in the three states following 6 steps/transitions, while assuming the initial position is node 3. (+20 points) 0.02 0.28 0.31 0.09 2.3 Which of the following probability distributions is a steady state of the system? Justify your answer (+15 points) 0.47 0.63 0.20 ГО.365 ГО.567 0.345 Lo.088. [0.365 0.298 0.336 0.33 Lo.336 Lo.298

Answer 1

Thae States n a Masker chain 2- Cullent states $3 3 2 2 1 !o.67 0.41 0-28 Marhor Matie P= 2 0.31 0.33 0-63 0.2 0.09 3 0.02 nent state (2.2) Given the initial peition is node 3 Hene the unitial Paobebility Vects is =°x. Pacbability Vectr aftu Slepe Haonistors 1 9X 0.47 O.67 0.28 O.63 O.33 O.31 O.09 O- 2 0.02 l0.5661 lo. 3454

peobability f being step teanitions 2ththree Stales Wemce the node 1-o. 566 nede 2 0.3454 mede 3 0.088 5 Stcady state Vectoi multiplied P then the hesult doey mot change that is ik x is the Steady state Vecter then Px=x This is tsue t O.567 0.34 5 0.088