By using the R-code to find out the stationary distribution is as followstherefore the stationary distribution is;
(0.2,0.4,0.2,0.2)
b) the answer is 0.4
c) we know that the relation between mean reccurence time and stationary distribution
and which is m32=1/v2
thus, m32=1/0.4=2.5
d) the probability that X1000=1 is 0.2
e) the mean reccurence time for state 1 is 1/v1=5
1. Consider a time-homogeneous Markov chain X)n, such that P= 2 a) Calculate p12(2) b) Assuming...
Suppose that we have a finite irreducible Markov chain Xn with stationary distribution π on a state space S. (a) Consider the sequence of neighboring pairs, (X0, X1), (X1, X2), (X2, X3), . . . . Show that this is also a Markov chain and find the transition probabilities. (The state space will be S ×S = {(i,j) : i,j ∈ S} and the jumps are now of the form (i, j) → (k, l).) (b) Find the stationary distribution...
Consider the following Markov chain with the following transition diagram on states (1,2,3 2 1/3 1 1/4 2 3 s this Markov chain irreducible? 1 marks (a) (b) Find the probability of the Markov chain to move to state 3 after two time steps, providing it starts in state 2 [3 marks 14 Find the stationary distribution of this Markov chain [4 marks (c) (d) Is the stationary distribution also a limiting distribution for this Markov chain? Explain your answer...
2. (10 points) Consider a continuous-time Markov chain with the transition rate matrix -4 2 2 Q 34 1 5 0 -5 (a) What is the expected amount of time spent in each state? (b) What is the transition probability matrix of the embedded discrete-time Markov chain? (c) Is this continuous-time Markov chain irreducible? (d) Compute the stationary distribution for the continuous-time Markov chain and the em- bedded discrete-time Markov chain and compare the two 2. (10 points) Consider 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.
1. Let (т, P) be a time-homogeneous discrete-time Markov chain with state space {1, . . . , (a) Show that the Markov chain is not stationary (i.e., SSS). (b) Suppose P is doubly stochastic and π- JJ, . . . , Đ. Then show that the Markov chain is stationary
A4. Classify the states of the Markov chain with the following transition matrix. 0 3 0 1 Find the stationary distribution of each irreducible, recurrent subchain and hence obtain the mean recurrence time of each state. (8
Consider the Markov chain with state space {0, 1,2} and transition matrix(a) Suppose Xo-0. Find the probability that X2 = 2. (b) Find the stationary distribution of the Markov chain
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....
Please give the detail solution to the problems. Let (T,P) be a time-homogeneous discrete-time Markov chain with state space {1, . . . ,J) (a) Show that the Markov chain is not stationary (i.e., SSS) (b) Suppose P is doubly stochastic and π = (1,7, . 1 . Then show that the Markov chain is stationary