L. Identify all absorbing states in the Markov chains having the following matrix. Decide whether the Markov chain is absorbing.
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Suppose that X0, X1, X2, ... form a Markov chain on the state space {1, 2}. Assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix of transition probabilities for the chain has the following entries: Q11 = 1/2, Q12 = 1/2, Q21 = 1/3, Q22 = 2/3. Find limn→∞ P(Xn = 1).. Suppose that a Markov chain with 3 states and with transition matrix P is in state 2 onthe second observation. Which of the following expressions represents the probabilitythat it will be in state 3 on the third observation? (A) the (2, 3) entry of P 3 (B) the (2, 3) entry of P 2(C) the (3, 3) entry of P 2 (D) the (2, 2) entry of P 3(E) the (2, 3) entry of P (F) the (3, 2) entry of P(G) the (3, 2) entry of P 3 (H) the (3, 2) entry of P 2
- A state vector XX for a three-state Markov chain is such that the system is as likely to be in state 3 as in state 1 and is five times as likely to be in state 2 as in 3. Find the state vector XX.A state vector XX for a three-state Markov chain is such that the system is as likely to be in state 3 as in state 1 and is three times as likely to be in state 2 as in 3. Find the state vector XX.Consider the Markov chain with three states,S={1,2,3}, that has the following transition matrix If we know P(X1=1) =P(X1=2) =1/4, find P(X1=3, X2=2,X3=1)
- A state vector XX for a three-state Markov chain is such that the system is as likely to be in state 3 as in state 1 and is four times as likely to be in state 2 as in 3. Find the state vector XX.If A is a Markov matrix, why doesn't I+ A+ A2 + · · · add up to (I -A)-1?1. A museum consists of six rooms of equal sizes arranged in the form of a grid with three rows and two columns. Each interior wall has a door that connects to adjacent rooms. Guards move through the rooms through the interior doors. Represent the movements of each guard in the museum as a Markov chain, and show that his states are periodic with period t = 2.
- For a Markov matrix, the sum of the components of x equals the sum of the components of Ax. If Ax = AX with,\ cf= 1, prove that the components of this non-steady eigenvector x add to zero.Consider the Markov chain having a three state space, namely {E0,E1,E2}{E0,E1,E2} and transition matrix PP, 3-state Markov chain P E_0 E_1 E_2 E_001/21/2E_11/43/40E_21/201/2 Compute p(2)10p10(2) Select one: a. 0.0250.025 b. 3/83/8 c. 00 d. (0.5)2For the attached transition probability matrix for a Markov chain with {Xn ; n = 0, 1, 2,.........}: a) How many classes exist, and which two states are the absorption states? b) What is the limn->inf P{Xn = 3 | X0 = 3}? b) What is the limn->inf P{Xn = 1 | X0 = 3}?