If the initial state probability distribution of Markov chain is ( ) ( )and transition probability matrix of the chain is ( ). Compute theprobability distribution of the chain after 2 steps

Consider a Markov chain with two states and transition probability matrix P = (0 11 0). Find thestationary distribution of the chain

Quiz question For each of the following transition matrices for Markov chains with state spaceS = {1, 2}, write down the Full Balance Equations and find the equilibrium distribution(s).(a) P =0.4 0.60.8 0.2(b) P =0.82 0.180.82 0.18

Quiz Question Consider the Markov chain with transition diagram345210.10.50.50.60.30.50.20.40.30.50.50.20.4i.e., with transition matrixP =0.6 0.4 0 0 00.5 0.5 0 0 00 0.5 0 0.5 00 0.5 0.3 0 0.20 0.1 0.2 0.4 0.3 .(a) Starting from state 5, what is the most likely two-step path? What is the probability(starting from state 5) of following that two-step path?(b) In this Markov chain, can you get from every state to every other state eventually?

. A Markov chain (Xn, n = 0, 1, . . . ) has state space S = {1, 2, 3, 4} and transition matrixP =0 2/5 3/5 01/4 0 1/2 1/40 3/4 0 1/40 0 0 1(a) Draw the transition diagram for this Markov chain. [2 marks](b) Find P (X3 = 1 | X0 = 1, X1 = 2, X2 = 1). [1 mark](c) Find P (X1 = 2, X2 = 1, X3 = 3, X4 = 4 | X0 = 3).

Given a transition matrix [[0.6, 0.3, 0.1], [0.2, 0.5, 0.3], [0.2, 0.4, 0.4]] for states [Person, Organization, Location], calculate the probability of transitioning from 'Person' to 'Organization' and then to 'Location'.Question 9Answera.0.09b.0.3c.0.6d.0.06