4. Consider the following transition matrix: 1 2 3 4 5 6 1 0 0 1 0 0 0 2 1 0 0 0 0 0 3 0 .5 00.5 ...
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 Markov chain {YmJnEN with state space S ,2, 3, 4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 00 1/6 1/2 1/3 0 0 4/9 4/9 1/9 0 0 5/6 1/6 (a) Find the equilibrium probability distribution π (b) Find the probability PO1 3. Уг 3.Ý, 1) Consider a Markov chain {YmJnEN with state space S ,2, 3, 4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 00 1/6 1/2 1/3 0 0 4/9...
Question 5 9 marks Consider a Markov chain {YTheN with state space S = {1,2,3,4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 0 0 p 1/6 1/2 1/30 0 4/9 4/9 1/9 0 0 5/6 1/6 2(a) Find the equilibrium probability distribution T (b) Find the probability P(-1%-3. Ya-1). Question 5 9 marks Consider a Markov chain {YTheN with state space S = {1,2,3,4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 0 0 p...
2. Consider a Markov chain with state space S 1,2,3,4) with transition matrix 1/3 2/3 0 0 3/4 1/4 00 0 0 1/5 4/5 0 0 2/3 1/3, (a) (10 points) Is the Markov chain irreducible? Explain your answer ive three examples of stationary distributions.
1. Consider a Markov chain (X) where X E(1.2,3), with state transition matrix 1/2 1/3 1/6 0 1/4 (a) (6 points) Sketch the associated state transition diagram (b) (10 points) Suppose the Markov chain starts in state 1. What is the probability that it is in state 3 after two steps? (c) (10 points) Caleulate the steady-state distribution (s) for states 1, 2, and 3, respee- tively 1. Consider a Markov chain (X) where X E(1.2,3), with state transition matrix...
Consider a Markov chain with transition matrix where 0< a, b,c <1. Find the stationary distribution.
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...
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.
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
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...