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

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?

In an office complex of 1180 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 78% chance that she will be at work tomorrow, and if the employee is absent today, there is a 54% chance that she will be absent tomorrow. Suppose that today there are 955 employees at work. (a) Find the transition matrix for this scenario (assume that state 1 is "at work" and state 2 is "absent"). [ ? ? , ? ?] (b) Predict the number that will be at work five days from now. ? (c) Find the steady-state vector. (Note that the sum of the entries must be the total number of employees, but make sure that your answers are correct to at least 1 decimal place.) [? ?]

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

A particle moves in a circle through points that have been marked 0, 1, 2, 3, 4 in a clockwise direction.order. The particle starts at point 0. At each step it has probability 0.35 of moving one point clockwise (0follows 4) and 0.65 of moving one point counter clockwise.Let Xn denote its location on the circle after step n.a). Construct the one step transition matrix for Xn.b) . Determine n-step transition matrix for n =5.

. 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).