Q.5 6 marks Markov chain with the following (a) Draw the state transition diagram for transition matrix P 0 0.5 0 0.5 0...
-1,2,3,4,5,63 and transition matrix Consider a discrete time Markov chain with state space S 0.8 0 0 0.2 0 0 0 0.5 00 0.50 0 0 0.3 0.4 0.2 0.1 0.1 0 0 0.9 0 0 0 0.2 0 0 0.8 0 0.1 0 0.4 0 0 0.5 (a) Draw the transition probability graph associated to this Markov chain. (b) It is known that 1 is a recurrent state. Identify all other recurrent states. (c) How many recurrence classes are...
Q.4 [8 marks] Consider the Markov chain with the following transition diagram 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain 1 marks 2 marks (b) Compute the two step transition matrix of the Markov chain (c) What is the state distribution T2 for t = 2 if the initial state distribution for 2 marks t 0 is o (0.1, 0.5, 0.4)T? 3 marks (d) What is the average time...
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix and initial distribution π = (0.2, 0.5, 0.3). Calculate P(X1 = 2) and P(X3 = 2|X0 = 0) 0.3 0.1 0.6 p0.4 0.4 0.2 0.1 0.7 0.2
Problem 7.4 (10 points) A Markov chain Xo, X1, X2,.. with state space S = {1,2,3,4} has the following transition graph 0.5 0.5 0.5 0.5 0.5 0.5 2 0.5 0.5 (a) Provide the transition matrix for the Markov chain (b) Determine all recurrent and all transient states (c) Determine all communication classes. Is the Markov chain irreducible? (d) Find the stationary distribution (e) Can you say something about the limiting distribution of this Markov chain? Problem 7.4 (10 points) A...
Consider the Markov chain with the following transition diagram. 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain (b) Compute the two step transition matrix of the Markov chain 2 if the initial state distribution for 2 marks (c) What is the state distribution T2 for t t 0 is To(0.1, 0.5, 0.4)7? [3 marks (d) What is the average time 1.1 for the chain to return to state 1?...
2. The Markov chain (Xn, n = 0,1, 2, ...) has state space S = {1, 2, 3, 4, 5} and transition matrix (0.2 0.8 0 0 0 0.3 0.7 0 0 0 P= 0 0.3 0.5 0.1 0.1 0.3 0 0.1 0.4 0.2 1 0 0 0 0 1 ) (a) Draw the transition diagram for this Markov chain.
Determine the equivalence classes and classify the states as transient or recurrent for a Markov chain with the following transition matrices c and d. Also determine the closed and irreducible subsets of the state space. 0 10.4 1 1 0 0.1 0.7 0.4 c) 0.1 0.3 10.3 0 0 0.3 0 0.2 0 0 0.5 0 0 0 0 0 0 d) 0 0.5 0.3 1 0 0.7 0.1 0.2 0 0 0 0 0.5 0 0 0 0 0...
2. The transition probabilities for several temporally homogeneous Markov chains with states 1,.,n appear below. For each: . Sketch a small graphical diagram of the chain (label the states and draw the arrows, but you do not need to label the transition probabilities) . Determine whether there are any absorbing states, and, if so, list them. » List the communication classes for the chain . Classify the chain as irreducible or not . Classify each state as recurrent or transient....
2. The transition probabilities for several temporally homogeneous Markov chains with states 1,.,n appear below. For each: . Sketch a small graphical diagram of the chain (label the states and draw the arrows, but you do not need to label the transition probabilities) . Determine whether there are any absorbing states, and, if so, list them. » List the communication classes for the chain . Classify the chain as irreducible or not . Classify each state as recurrent or transient....
A Markov chain X0, X1, X2,... has transition matrix 012 0 0.3 0.2 0.5 P = 1 0.5 0.1 0.4 .2 0.3 0.3 0.4 (i) Determine the conditional probabilities P(X1 = 1,X2 = 0|X0 = 0),P(X3 = 2|X1 = 0). (ii) Suppose the initial distribution is P(X0 = 1) = P(X0 = 2) = 1/2. Determine the probabilities P(X0 = 1, X1 = 1, X2 = 2) and P(X3 = 0). 2. A Markov chain Xo, Xi, X2,. has...