Consider the transition matrix [1/2 0 0 1/2] 0 1/2 0 1/20 0 1/4 0 3/4...
Consider the transition matrix [1/2 0 01/2 0 1/2 0 1/2 0 0 1/4 0 3/4 0 1/2 0 0 1/2 (a) Draw the transition diagram for the associated Markov chain (X(n)) and use it to determine whether the chain is irreducible. (b) Find the classes and determine whether each class is transient or ergodic. Determine whether each ergodic class is aperiodic or periodic (in which case determine its period). (e) Reorder the states and rewrite the transition matrix so...
5. (10 points) Exercise 13, Ch.6 of G, cither edition) Consider the transition matrix [1/2 00 1/2] 0 1/2 0 1/20 P-10 3/4 1/81/8 0 0 1/4 0 3/40 1/2 0 0 0 1/2 (a) Draw the transition diagram for the associated Markov chain (X(n)) and use it to deternine whether the chain is irreducible. (b) Find the classes and determine whcther each class is transient or ergodic. Determine whether each ergodlic class is aperiodic or periodic (in which case...
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....
Consider the Markov chains given by the following transition matrices. (1) Q = (1/2 1/2) (we= (1/2 162) (ii) Q = (1 o). /1/3 0 2/3 (1/2 1/2 0 (iv) Q = 1 0 1 0 1 (v) Q = 1 0 1/2 1/2 lo 1/5 4/5) \1/3 1/3 1/3) For each of the Markov chains above: A. Draw the transition diagram. B. Determine whether the chain is reducible or irreducible. Justify your answer. C. Determine whether the chain is...
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...
Consider the Markov chains with the following probability transition matrices: ar-(032) OP=(0503) a) P = 0.5 0.5 0.5 0.5 b) P = 0.5 1 1 0.5 0 OPEL c) P = 0 1 = 0 ( e) P = 0 d) P = WI-NI-NI- 11 Draw the transition diagram for each case and explain whether the Markov chain is irreducible and/or aperiodic.
A Markov chain {Xn,n 2 0) with state space S 10, 1, 2,3, 4,5) has transition proba- bility matrix 0 1/32/3-ββ/2 01-α 0 β/2 0 0 0 0 0 0 β/2 β/21/2 0 1. Y (a) Determine the equivalence classes of communicating states for any possible choice of the three parameters α, β and γ; (b) In all cases, determine if the states in each class are recurrent or transient and find their period (or determine that they are aperiodic)
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...
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2, 3, 4, 5} has transition probability matrix P. ain {x. " 0) with state spare S-(0 i 2.3.45) I as transition proba- bility matrix 01-α 0 0 1/32/3-3 β/2 0 β/2 0 β/2 β/21/2 0001-γ 0 0 0 0 (a) Determine the equivalence classes of communicating states for any possible choice of the three parameters α, β and γ; (b) In all cases, determine if...