In a laboratory experiment, a mouse can choose one of two food types each day, typeI or type II. Records show that if the mouse chooses type I on a given day, then there is a 75%chance that it will choose type I the next day, and if it chooses type II on one day, then there is a50% chance that it will choose type II the next day.(a) Find the transition matrix for this Markov chain. Is it regular? Remember this means thatall the entries of some power of the matrix are positive.(b) If the mouse chooses type I today, what is the probability that it will choose type I two daysfrom now?(c) If the mouse chooses type II today, what is the probability that it will choose type II threedays from now?(d) About what percentage of the time should we expect the mouse to choose type I food? TypeII?

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Answered: In a laboratory experiment, a mouse can…

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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At Suburban Community College, 40% of all business majors switched to another major the next semester, while the remaining 60% continued as business majors. Of all non-business majors, 20% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. (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.
A Markov Chain has the transition matrix 1 P = and currently has state vector ½ ½ . What is the probability it will be in state 1 after two more stages (observations) of the process? (A) 112 (B) % (C) %36 (D) 12 (E) % (F) 672 (G) 3/6 (H) "/2
Please help me answer this. Thank you.
(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.1. Assume that state 1 is high volume and that state 2 is low volume (1) Find the transition matrix for this Markov process. (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks?
Problem: Construct an example of a Markov chain that has a finite number of states and is not recurrent. Is your example that of a transient chain?
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.
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.
Cs401 3b
5

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