10. Consider the Marko chain (X0,.) with state space (0,1,2,3,4) and transition matris 0.2 0. 0.4...
1. A Markov chain {X,,n0 with state space S0,1,2 has transition probability matrix 0.1 0.3 0.6 P=10.5 0.2 0.3 0.4 0.2 0.4 If P(X0-0)-P(X0-1) evaluate P[X2< X4]. 0.4 and P 0-2) 0.2. find the distribution of X2 and
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2} has transition probability matrix 0.1 0.3 0.6 p = 0.5 0.2 0.3 0.4 0.2 0.4 If P(X0 = 0) = P(X0 = 1) = 0.4 and P(X0 = 2) = 0.2, find the distribution of X2 and evaluate P[X2 < X4].
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
Let (X.) be a Marko chain with the state space (1.2,3) and transition proba- bility matrix 0 4 6 P 25 75 0 4 0 6 Let the initial distribution be q(0) [1(0), q2(0), s(0) [0.4, 0.2, 0.4] (a) Find ELX. (b) Calculate PlX,-2, X,-2, X,-11X,-1]. (c) To what matrix will the n-step transition probability matrix converge when n is very large? Your solution should be accurate to two decimal places.
A Markov chain X0, X1, X2,... has transition matrix 012 0 0.3 0.2 0.5 P = 1 0.5 0.1 0.4 .2 0.3 0.3 0.4 (i) Determine the conditional probabilities P(X1 = 1,X2 = 0|X0 = 0),P(X3 = 2|X1 = 0). (ii) Suppose the initial distribution is P(X0 = 1) = P(X0 = 2) = 1/2. Determine the probabilities P(X0 = 1, X1 = 1, X2 = 2) and P(X3 = 0). 2. A Markov chain Xo, Xi, X2,. has...
-1,2,3,4,5,63 and transition matrix Consider a discrete time Markov chain with state space S 0.8 0 0 0.2 0 0 0 0.5 00 0.50 0 0 0.3 0.4 0.2 0.1 0.1 0 0 0.9 0 0 0 0.2 0 0 0.8 0 0.1 0 0.4 0 0 0.5 (a) Draw the transition probability graph associated to this Markov chain. (b) It is known that 1 is a recurrent state. Identify all other recurrent states. (c) How many recurrence classes are...
2. The Markov chain (Xn, n = 0,1, 2, ...) has state space S = {1, 2, 3, 4, 5} and transition matrix (0.2 0.8 0 0 0 0.3 0.7 0 0 0 P= 0 0.3 0.5 0.1 0.1 0.3 0 0.1 0.4 0.2 1 0 0 0 0 1 ) (a) Draw the transition diagram for this Markov chain.
(Only need help with parts b and c) Consider the transition matrix If the initial state is x(0) = [0.1,0.25,0.65] find the nth state of x(n). Find the limn→∞x(n) (1 point) Consider the transition matrix 0.5 0.5 0.5 P 0.3 0.3 0.1 0.2 0.2 0.4 10 a. Find the eigenvalues and corresponding eigenvectors of P. ,-| 0 The eigenvalue λι The eigenvalue λ2-1 The eigenvalue A3 1/5 corresponds to the eigenvector vi <-1,1,0> corresponds to the eigenvector v2 = <2,1,1>...
Consider the Markov chain X0,X1,X2,... on the state space S = {0,1} with transition matrix P= (a) Show that the process defined by the pair Zn := (Xn−1,Xn), n ≥ 1, is a Markov chain on the state space consisting of four (pair) states: (0,0),(0,1),(1,0),(1,1). (b) Determine the transition probability matrix for the process Zn, n ≥ 1.
Consider a Markov chain with state space S = {0, 1, 2, 3} and transition probability matrix P= (a) Starting from state 1, determine the mean time that the process spends in each transient state 1 and 2, separately, prior to absorption. (b) Determine the mean time to absorption starting from state 1. (c) Starting from state 1, determine the probability for the process to be absorbed in state 0. Which state is it then more likely for the process...