A Markov chain {Xn,n 2 0) with state space S 10, 1, 2,3, 4,5) has transition...
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2, 3, 4, 5} has transition probability matrix P. ain {x. " 0) with state spare S-(0 i 2.3.45) I as transition proba- bility matrix 01-α 0 0 1/32/3-3 β/2 0 β/2 0 β/2 β/21/2 0001-γ 0 0 0 0 (a) Determine the equivalence classes of communicating states for any possible choice of the three parameters α, β and γ; (b) In all cases, determine if...
1. A Markov chain (x,, n 2 01 with state space S (0,1,2,3,4,5] has transition proba- bility matrix Γα β/2 01-α 0 0 0 0 1/32/3_ββ/2 β/2 β/2 1/2 0 0 0 0 (a) Determine the equivalence classes of communicating states for any possible choice of the three parameters α, β and γ; (b) In all cases, determine if the states in each class are recurrent or transient and find their period (or determine that they are aperiodic)
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....
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 0.2 0.8 0 0 O P = \ 0 0.1 0 0.2 0.7 0 0.9 0 0.1 0 0 0 0 0 1 on five states 1,2,3,4,5} 2 marks (b) Identify the communicating classes of the Markov chain and identify whether they are open or closed. Write them in set notation and mark them on the transition...
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...
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....
1. Let Xn be a Markov chain with states S = {1, 2} and transition matrix ( 1/2 1/2 p= ( 1/3 2/3 (1) Compute P(X2 = 2|X0 = 1). (2) Compute P(T1 = n|Xo = 1) for n=1 and n > 2. (3) Compute P11 = P(T1 <0|Xo = 1). Is state 1 transient or recurrent? (4) Find the stationary distribution à for the Markov Chain Xn.
The possible transitions between the states of a Markov chain are shown in the diagram belo The communicating classes are (1, 2). (3, 4) and (5, 6, 7 Select the option that gives a correct description of the class (3,4) Select one: Closed, recurrent, aperiodic Closed, transient, aperiodic Closed, recurrent, periodic with period 2 Closed, transient, periodic with period 2 Not closed, recurrent, aperiodic Not closed, transient, aperiodic. Not closed, recurrent, periodic with period 2 Not closed, transient, periodic with...
The possible transitions between the states of a Markov chain are shown in the diagram belo The communicating classes are (1, 2). (3. 4) and (5. 6. 7 Select the option that gives a correct description of the class (3,4) Select one: Closed, recurrent, aperiodic Closed, transient, aperiodic Closed, recurrent, periodic with period 2 Closed, transient, periodic with period 2 Not closed, recurrent, aperodic Not closed, transient, aperiodic Not closed, recurrent periodic with period 2 Not closed, transient, periodic with...
The possible transitions between the states of a Markov chain are shown in the diagram belo The communicating classes are (1, 2). (3. 4) and (5. 6. 7 Select the option that gives a correct description of the class (3,4) Select one: Closed, recurrent, aperiodic Closed, transient, aperiodic Closed, recurrent, periodic with period 2 Closed, transient, periodic with period 2 Not closed, recurrent, aperodic Not closed, transient, aperiodic Not closed, recurrent periodic with period 2 Not closed, transient, periodic with...