Let (X0, X1, X2, . . .) be the discrete-time, homogeneousMarkov chain on state space S = {1, 2, 3, 4, 5} with X0 = 3 and transition matrix 101/4 00000001/41/2 01/6 1/6 1/201/2 1/2000 11/60(a) Calculate P(X10 = 2 | Xg = 4).8(b) Calculate the probability that the chain is absorbed in state 5.T-1(c) Calculate ExtXt where T is the time of absorption.t=0(d) Explain why this chain has infinitely many equilibrium distributions.

is the discrete-time, homogeneous Markov chain.State space Initial State, The transition matrix:

Answered: 1 1/4 0 0 0 0 0 0 0 0 1/2 0 1/4 1/6 1/6…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find the limiting distribution for this Markov chain.
4. Let X be a Markov chain with state space S = {1, 2, 3) and transition matrix (² where 0 < p < 1. Prove that P = 0 Ph = P P P 1-P 0 0 P 1-p ain a2n a3n aln a2n a3n where ain + wa2n + w²a3n = (1 − p + pw)", w being a complex cube root of 1. a3n a2n ain
A Markov chain {s} with state space n={1, 2, 3} has a sequence of realizations and process transitions as follows: Transition (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3.1) (3,2) (3,3) t S: S+1 2 1 1. 1 1 1 1 1 3 1 3 3 3 4 3 1. 2 3 1. 2 1 7 2 2 1. 8 2 2 1 9 2 3 1. 10 3 11 1 1 12 1 1. 13 1 1. 14 1. 1. 15 3 1. 1. 16 1. Number of frequencies : 1 3. 2 2 1 1 1 1 a. determine the transition frequency matrix O= 2 12 93 021 022 °23 %3D 31 °32 °33) 1 P1 P12 P13 b. determine the estimated transition probability matrixP= 2 P21 P22 P23 3 P31 P32 P33)
The sequence (Xn)n>o is a Markov chain with transition matrix 0 을 0 0 0 3 1 0 0 0 4 4 0 } 0 0 0 1 2 1 1 0 0 3 3 0 } 0 } 0 0 0 0 0 0 0 (a) Draw the transition diagram for (Xn). (b) Determine the communicating classes of the chain, stating whether each class is recurrent or transient. (c) Determine the period of each communicating class.
Consider a continuous-time Markov chain whose jump chain is a random walk with reflecting barriers 0 and m where po,1 = 1 and pm,m-1 =1 and pii-1 = Pii+1 = for 1
(6) Give an example of a Markov chain Xn on a countable state space S and a function g on S such that g(Xn) is not a Markov chain. Can you give any conditions on Xn and g which ensure that g(Xn) is a Markov chain?
Recall that the graph of a discrete-time, finite-state, homogeneous Markov chain on two states 1, 2 with transition matrix is CO (: :) 1 T = If instead a new Markov chain on three states {1, 2, 3} has transition matrix 10 1 0 (a) Draw the corresponding graph for this new Markov chain. (b) Is the Markov chain with transition matrix T irreducible?
Let (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5, 6} with X0 = 1 and transition matrix
IN Markov process having transition matrix A = [a,k], whose entries are a11 = a12 = 0.6,a21 = 0.8, a22 = 0.8. and the initial state [0.7 0.8]T, SOLVE FOR the next 3 states.
C)
2. For all permissible p values, determine the equivalence classes of the Markov chain with the following transition matrix P, classify states as transient or recurrent, and classify the Markov chain as irreducible or reducible. 0. 1-p 1 - 0. P = 0. 1-p 0. 1-p
1. Prove that Weiner Process is Markovian (Markov Process).

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