2. Write a stochastic matrix corresponding to the following transition diagram: .8 3. Draw a transition...
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...
linear algebra Another use of the transition matrix is in stochastic modeling. An example is the following: Imagine a park with three locations: a lake; a picnic area; and a playground. Every hour, on the hour, the parkgoers move according to the following rulcs: Half of those at the lake move to the picnic area, and one-quarter of those at the lake move to the playground. Half of those at the picnic area go to the lake, and the other...
This Decide whether the given matrix could be a transition matrix. If so, sketch a transition diagram. А B с 0.1 0.2 0.7 PE B 0 1 0 с 0.4 0.4 0.2 Identify the transition diagram ОА. ов. 7 Ос. OD. The given matrix is not a transition matrix, so there is no di fc det us a sy Click to select your answer. sor
Consider an Ehrenfest chain with 6 particles. (a) Write down the transition matrix and draw the transition diagram. b) If the chain starts with 3 particles in the left partition, write down the state distribution at the first time step. (c) Find the stationary distribution using the detailed balance condi tion Consider an Ehrenfest chain with 6 particles. (a) Write down the transition matrix and draw the transition diagram. b) If the chain starts with 3 particles in the left...
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?...
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...
1.13. Consider the Markov chain with transition matrix: 1 0 0 0.1 0.9 2 0 0 0.6 0.4 3 0.8 0.2 0 0 4 0.4 0.6 0 0 (a) Compute p2. (b) Find the stationary distributions of p and all of the stationary distributions ofp2. (c) Find the limit of p2n(x, x) as n → oo.
1. Consider an Ehrenfest chain with 6 particles. (a) Write down the transition matrix and draw the transition diagram. (b) If the chain starts with 3 particles in the left partition, write down the state distribution at the first time step. (c) Find the stationary distribution using the detailed balance condition.
Decide whether the matrix could be a transition matrix, by definition. Sketch a transition diagram for any transition matrix. 1 Decide whether the matrix 99 could be a transition matrix, by definition, Sketch a transition diagram for any transition matrix 1 O 2 1 Could the matrix be a transition matrix? 1 0 Yes No Which of the following is the transition diagram for this matrix? ОА. ов. 0 2/9 COLOD color Cobos C This matrix has no transition diagram...
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