Consider a biased random walk with reflecting boundaries on {1, 2, 3, 4) with probability p=0.45 of moving to the left.a. Find the transition matrix for the Markov chain and show that this matrix is not regular.b. Assuming that the steady-state vector may be interpreted as occupation times for this Markov chain, in what state will this chainspend the most steps?a. The transition matrix is P = -(Type an integer or simplified fraction for each matrix element.)

a. The state space of the Markov chain consists of the four possible positions: {1,2,3,4}. Let P…

Answered: Consider a biased random walk with…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A Markov Chain has the transition matrix P 3D 0. 1 and currently has state vector % %% . What is the probability it will be in state 1 after two more stages (observations) of the process? 6. (A) % 3/4 (B) 0 1/12 (D) ½4 (E) 2 /12 1/4 (G) 1 (H) 23/24 O A O B OD O E OF OG H.
Determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.
Consider the Markov chain with state space S = {0, 1, 2,...} and transition probabili- ties Poo = 1 - P. P02 = P, and Pr,x+2= P₁ P2,2-1=1-p, for x = 1,2,... For which values of p is this a transient chain?
If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. %3D
A factory worker will quit with probability 1/2 during her first month, with probability 1/4 during her second month and with probability 1/8 after that. Whenever someone quits, their replacement will start at the beginning of the next month. Model the status of each position as a Markov chain with 3 states. Identify the states and transition matrix. Write down the system of equations determining the long-run proportions. Suppose there are 900 workers in the factory. Find the average number of the workers who have been there for more than 2 months.
For the attached Markov chain with the following transition probability matrix: The Markov chain has only one recurrent class. Determine the period of this recurrent class.
A Markov chain has two states. • If the chain is in state 1 on a given observation, then it is three times as likely to be in state 1 as to be in state 2 on the next observation. If the chain is in state 2 on a given observation, then it is twice as likely to be in state 1 as to be in state 2 on the next observation. Which of the following represents the correct transition matrix for this Markov chain? О [3/4 2/3 1/4 1/3 O [2/3 1/3 3/4 1/4) о [3/4 2/3 1/3] None of the others are correct 3/4 O [1/4 1/3 2/3. O [3/4 1/4] 1/3 2/3.
Find the limiting distribution for this Markov chain. Then give an interpretation of what the first entry of the distribution you found tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology.
Please show solutions and explain steps
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.
Consider the Markov chain with three states,S={1,2,3}, that has the following transition matrix 1.Draw the state transition diagram for this chain. (10 marks)
At Suburban Community College, 30% of all business majors switched to another major the next semester, while the remaining 70% continued as business majors. Of all non-business majors, 10% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. HINT [See Example 1.] (Let 1 business majors, and 2 = non-business majors.) = Calculate the probability that a business major will no longer be a business major in two semesters' time.

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