Question: Consider a Markov chain with state space S = {1, 2, ...,6} and transition matrix given by OOOHNIH O OAIW ONIH P = O O

Consider a Markov chain with state space S = {1, 2, ...,6} and transition matrix given by OOOHNIH O OAIW ONIH P = O O OAIHO O O ONIHO O O WIN ONIHO O O WIHHOOOO (a) Find all stationary distributions for this chain (b) Find the probability that we ever reach state 1, starting from state 3 (c) Find the expected time that we first reach the set of states A = {2, 5}, starting from state 3. (d) Starting from state 3, find the limiting proportion of time spent in state 1. (e) Starting from state 3, find the expected limiting proportion of time spent in state 1. (f) Repeat the above two questions, starting from state 4 instead of state 3

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

answer all questions Consider a Markov chain with state space S = {1, 2, ...,6} and transition matrix given by P = O O OAKW ONIN O ONIHO O O OO OO HNIH O O OAIHO O WITHOOOO WIN ONIHO O O (a) Find all...

Markov chain irreducible 2. A Markov chain with state space {1, 2, 3} has transition probability matrix 00 0.3 0.1 a: 0.3 0.3 0.4 0.4 0.1 0.5 (a) Is this Markov chain irreducible? Is the Markov chain...

1.In a certain department of a factory there are two shops. Total departmental overheads for a year are `1,20,000 and the estimated number of direct labour hour is 24,000 (10 men employed for 48...

b) We are interested in estimating and constructing a confidence interval for the percentage change in price when a 200-square-foot bedroom is added to a house. How can you construct this confidence...

Reorder the states in the Markov chain in Exercise 6 to produce a transition matrix in canonical form. Data From Exercise 6 In Exercises 16, consider a Markov chain with state space with {1;...

Reorder the states in the Markov chain in Exercise 1 to produce a transition matrix in canonical form. Data From Exercise 1 In Exercises 16, consider a Markov chain with state space with {1;...

Reorder the states in the Markov chain in Exercise 2 to produce a transition matrix in canonical form. Data From Exercise 2 In Exercises 16, consider a Markov chain with state space with {1;...

In Exercises 16, consider a Markov chain with state space with {1; 2,......, n} and the given transition matrix. Identify the communication classes for each Markov chain as recurrent or transient,...

Let A and B be positive definite symmetric n ( n matrices and let c be a positive scalar. Show that the following matrices are positive definite. (a) cA (b) A2 (c) A + B (d) A-1 (First show that A is...

What would be the output generated by the following code? import java.util.concurrent.*; public class Main { public static void main (String [] args) { new ConcurrentHashMap (); ConcurrentHashMap chm...

What stands out about the Emergency Banking Act, passed in March 1 9 3 3 ?

Firm X is solely financed by $1 million equity at cost of 10%. X wants to raise $0.6 million debt at cost of 4% and use all of it to buy back outstanding equity. a) In a perfect capital market, what...

(Appendices) Many employers have both group short-term and long-term disability-income plans. Compare (1) short-term plans with (2) long-term plans with respect to each of the following: LO8 a....

(Appendices) Brandon, age 32, is married and has a son, age one. Six months ago, Brandon purchased an individual health insurance policy covering the entire family. His son was recently diagnosed...

(Appendices) Ken, age 52, works only part-time and has no health insurance. The cartilage in both his knees is severely eroded from osteoarthritis, which causes severe pain during his daily...