A continuous time markov chain has generator matrix Q=[-1,1,0; 1, -2, 1; 2, 2, -4]. Exhibit the transition matrix of the embedded markov chain and ii) the holding time parameter for each state
A continuous time markov chain has generator matrix Q=[-1,1,0; 1, -2, 1; 2, 2, -4]. Exhibit...
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...
Consider a three-state continuous-time Markov chain in which the transition rates are given by The states are labelled 1, 2 and 3. (a) Write down the transition matrix of the corresponding embedded Markov chain as well as the transition rates out of each of the three states. (b) Use the symmetry of Q to argue that this setting can be reduced to one with only 2 states. (c) Use the results of Problem 1 to solve the backward equations of...
Consider a three-state continuous-time Markov chain in which the transition rates are given by The states are labelled 1, 2 and 3. (a) Write down the transition matrix of the corresponding embedded Markov chain as well as the transition rates out of each of the three states. (b) Use the symmetry of Q to argue that this setting can be reduced to one with only 2 states. (c) Use the results of Problem 1 to solve the backward equations of...
7.7 A Markov chain has generator matrix -0 0-0-2 2 3 0-3 (a) Exhibit the Kolmogorov backward equations. b) Find the transition function by diagonalizing the generator and finding the matrix exponential
7.3 A three-state Markov chain has distinct holding time parameters a, b, and c From each state, the process is equally likely to transition to the other two states. Exhibit the generator matrix and find the stationary distribution.
Problem 5.2 (10 points) A three-state Markov chain with state space S = {1,2,3} has distinct holding time parameters 91 = 1, 92 = 2, and q3 = 3. From each state, the process is equally likely to transition to the other two states. Exhibit the generator matrix and find the stationary distribution.
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...
Consider a Markov chain with state space S = {1, 2, 3, 4} and transition matrix P= where (a) Draw a directed graph that represents the transition matrix for this Markov chain. (b) Compute the following probabilities: P(starting from state 1, the process reaches state 3 in exactly three time steps); P(starting from state 1, the process reaches state 3 in exactly four time steps); P(starting from state 1, the process reaches states higher than state 1 in exactly two...
Xn is a discrete-time Markov chain with state-space {1,2,3}, transition matrix, P = .2 .1 .7 .3 .3 .4 .6 .3 .1 and initial probability vector a = [.2,.7,.1]. The P(X2=2) =
P is the (one-step) transition probability matrix of a Markov chain with state space {0, 1, 2, 3, 4 0.5 0.0 0.5 0.0 0.0 0.25 0.5 0.25 0.0 0.0 P=10.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.5 0.5/ (a) Draw a transition diagram. (b) Suppose the chain starts at time 0 in state 2. That is, Xo 2. Find E Xi (c)Suppose the chain starts at time 0 in any of the states with...