Consider the following discrete-time Markov chain with initial state 3.of12221123721245(a) What are the communicating classes?(b) For each communicating class, determine the period and whether it is transient or recurrent.(c) Write down the state transition matrix P.T(d) Does a unique limiting state probability vector a exist? If so, argue why and solve for it. Ifnot, argue why.

a. Communicating Classes:Communicating classes are groups of states within a Markov chain where each…

Answered: Consider the following discrete-time…

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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The transition matrix of a Markov Process is given by .4 2 T = .3 y .2 .3 .4 (a) Enter the values of the unknowns in the boxes below: X = Number y = Number z = Number .2 (b) The initial distribution vector is v = .5 .3 Enter the distribution vector after one time unit in the box below:
DO NOT COPY OTHER SOLUTIONS. USE A TRANSITION PROBABILITY MATRIX WHEN SOLVING. Consider the following Markov chain. Assuming that the process starts in state 4, what is the probability that we eventually reach the recurrent class {1,2}?
Employment Employment Last Year This Year Percentage Industry Industry 80 Small Business 10 Self-Employed 10 Small Business Industry 10 Small Business 60 Self-Employed 30 Self-Employed Industry 10 Small Business 80 Self-Employed 10 Assume that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed. Find the transition matrix for this Markov process. P =
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Anne and Barry take turns rolling a pair of dice, with Anne going first. Anne’s goal is to obtain a sum of 3, while Barry’s goal is to obtain a sum of 4. The game ends when either player reaches his goal,and the one reaching the goal is the winner. Define a Markov Chain to model the problem.
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A Markov chain has the transition matrix shown below: 0.2 0.1 0.7] P = 0.6 0.4 1 (Note: For questions 1, 3, and 5, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the next observation? (2) If, on the first observation the system is in state 1, what state is the system most likely to occupy on the next observation? (If there is more than one such state, which is the first one.) (3) If, on the first observation, the system is in state 1, what is the probability that the system is in state 1 on the third observation? ...
Determine whether the statement below is true or false. Justify the answer. If (x) is a Markov chain, then X₁+1 must depend only on the transition matrix and xn- Choose the correct answer below. O A. The statement is false because x, depends on X₁+1 and the transition matrix. B. The statement is true because it is part of the definition of a Markov chain. C. The statement is false because X₁ +1 can also depend on X-1 D. The statement is false because X₁ + 1 can also depend on any previous entry in the chain.
For the following Markov models: a ito dove b) find the stationary probability distribution on paper, SUre 5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. 5B An individual can be either susceptible or infected, the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. 5C The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.

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