1. Let {Xt,t 0,1,2,...J be a Markov chain with three states (S 1,2,3]), initial distribution (0.2,0.3,0.5)...
Let Xn be a Markov chain with state space {0,1,2}, the initial probability vector and one step transition matrix a. Compute. b. Compute. 3. Let X be a Markov chain with state space {0,1,2}, the initial probability vector - and one step transition matrix pt 0 Compute P-1, X, = 0, x, - 2), P(X, = 0) b. Compute P( -1| X, = 2), P(X, = 0 | X, = 1) _ a. 3. Let X be a Markov chain...
For the next three problems, consider a Markov chain (Xn n2o with three states 1,2,3: 「0.5 0.3 0.2 P 0.1 0.4 0.5 0 0.2 0.8 ANDREY SARANTSEV Problem 11.24. Calculate the probability P(X2X 1) Problem 11.25. For the initial distribution x(0) 10.6, 0.1,이, find the distribution of Xi Problem 11.26. Find the stationary distribution
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].
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
(10 points) Consider a Markov chain (Xn)n-0,1,2 probability matrix with state space S ,2,3) and transition 1/5 3/5 1/5 P-0 1/2 1/2 3/10 7/10 0 The initial distribution is given by (1/2,1/6,1/3). Compute (a) P[X2-k for all k- 1,2,3 (b) E[X2] Does the distribution of X2 computed in (a) depend on the initial distribution a? Does the expected value of X2 computed in (b) depend on the nitial distribution a? Give a reason for both of your answers.
1. Let Xn be a Markov chain with states S = {1, 2} and transition matrix ( 1/2 1/2 p= ( 1/3 2/3 (1) Compute P(X2 = 2|X0 = 1). (2) Compute P(T1 = n|Xo = 1) for n=1 and n > 2. (3) Compute P11 = P(T1 <0|Xo = 1). Is state 1 transient or recurrent? (4) Find the stationary distribution à for the Markov Chain Xn.
(2.) A discrete-tim e Markov chan X, E {0,1,2) has the following transition probability matrix: 0.1 0.2 0.7 P-10.8 0.2 0 0.1 0.8 0.1 Suppose Pr(Xo = 0) = 0.3, Pr(X,-1) = 0.4, and Pr(Xo = 2) = 0.3. Compute the following. .lrn( (a) Pr (X0-0, X,-2, X2-1). (b) Pr(X2-iXoj) for all i,j
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...
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