General question regarding Markov chain states...
What is the period of a transient state? As in the formula.
Is it just the finite mean of the geometric distribution: 1/(1-fi) ?
Transient state can never return the same state. Hence period of transient state is zero.
General question regarding Markov chain states... What is the period of a transient state? As in...
Suppose a Markov chain has state space S (0, 1,2) and states 0 and 1 are known to be transient. No matter where you start, describe what must happen to any sample (with probability 1) as n- co and why. Explain carefully. Suppose a Markov chain has state space S (0, 1,2) and states 0 and 1 are known to be transient. No matter where you start, describe what must happen to any sample (with probability 1) as n- co...
3. (5 points) Since the long-run proportion of time that a Markov chain spends in a transient state is 0, there doesn't exist an irreducible Markov chain with all the states being transient. Is it true? If not, please give a counterexample. 3. (5 points) Since the long-run proportion of time that a Markov chain spends in a transient state is 0, there doesn't exist an irreducible Markov chain with all the states being transient. Is it true? If not,...
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...
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...
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, 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...
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...
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....