Let (Xn)nzo be a Markov chain with state space S = {A, B, C} and transition matrix P given byCompute PBB, n € N.P=14 12 L14D| D|- NITAT A L12 44 412

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Answered: Let (Xn)nzo be a Markov chain with…

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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For the attached transition probability matrix for a Markov chain with {Xn ; n = 0, 1, 2,.........}: a) How many classes exist, and which two states are the absorption states? b) What is the limn->inf P{Xn = 3 | X0 = 3}? b) What is the limn->inf P{Xn = 1 | X0 = 3}?
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.
(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?
Suppose you have two urns with a total of 5 balls. At each step, one of the five balls is chosen at random and switched from its urn to the other urn. Let X, be the number of balls in the first urn after n switches. a) Is {X, : n = 1,2,...} a Markov Chain? Explain. b) Define the state space and provide the one step transition matrix. c) Draw the corresponding transition graph. d) Classify the states. Are there any periodic states? e) What is the probability that, given I have 3 balls in the first urn at the 10th turn, I will have 2 balls at the 12th turn?
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
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
Please answer #28 and explain your reasoning.
1. Prove that Weiner Process is Markovian (Markov Process).
A box contains 1 red pen and 2 blue pens. Every time, a pen is selected at random from the box and replaced with a pen of the opposite color, until all the pens in the box have the same color. Build the transition matrix O red 1 red 2red 3 red O red 1 red 2 red 3 red 1/2 1 1/3 2/3 1/4 || 3/4
A path of length k in a Markov chain {X,,n= 0,1,...} is a sequence of states visited from step n to step n+k. Let pij be the transition probability from state i to state j. Show that starting from state i,, the probability that the chain follows a particular path i, - i„.1 - in2 - ... - i,t is given by %3D "x*\":= "X)d = i2.,Xpsk = inrk | X, = i,) n+1 n+l> n+2 n+k = P Pu.

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Let (Xn)nzo be a Markov chain with state space S = {A, B, C} and transition matrix P given by ||| Compute PBB, nЄN. P = TIL FIN