6. A Markov chain has two non-absorbing states, A and B, and two absorbing states, C and D.Below are the one-cycle transition probabilities:from A to A: 10%from A to B: 20%from A to C: 50%from A to D: 20%from B to A: 40%from B to B: 20%from B to C: 10%from B to D: 30%(a) Draw a diagram showing the states and the possible one-cycle transitions. Make sure tomark the appropriate probabilities.

Given information: The transition probabilities are, P(A to A)=10%=0.10 P(A to B)=20%=0.20 P(A to…

Answered: 6. A Markov chain has two non-absorbing…

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 following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 3 after three periods is a. 0.259 b. 0.261 c. 0.283 d. 0.296
Appointments in a medical office are scheduled every 15 minutes. Throughout the day, appointments will be running on time or late, depending on the previous appointment only, according to the following matrix of transition probabilities: Previous Appointment Next Appointment On Time Late On Time .70 .30 Late .45 .55 What are the steady state probabilities?
Consider the Markov chain specified by the following transition diagram. a. Find the steady-state probabilities of all states. 0.4 b. If the initial state is 7, what is the expected 0.3 0.4 0.2 number of steps to reach state 1 or 3? 0.8 0.2 c. If at step 0 the system was in state 4, what is the probability that after step 3 it was in state 3 and after step 47 it was in state 3 again?
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.
The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 2 after two periods is a. 0.283 b. 0.26 c. 0.261 d. 0.47
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Suppose a two state experiment has the following transition matrix: 0.2] 0.4 0.8 P = 0.6 Answer the following questions: 1. Find P(2). ... ... ... ... ... 2. If the experiment is in state 1 on the first observation, what is the probability that it will be in state 2 on the third observation? ... ... 3. If the experiment is in state 1 on the first observation, what is the probability it is in state 2 on the next two observations? ...
an 15 A continuous-time Markov chain (CTMC) has three states (1, 2, 3). ed dout of The average time the process stays in states 1, 2, and 3 are 3, 11.9, and 3.5 seconds, respectively. question The steady-state probability that this CTMC is in the second state ( , ) is
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ne bets $1. 0.45, he wins the game and with probability 1 - p = 0.55, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
Given the following Markov Chain diagram. 0.15 On Duty Off 0.85 0.2 Duty 0.8 Given that you were on duty the first day (i.e., P(Day 1=On Duty) = 1 and P(Day %3D 1= Off Duty) = 0), answer the following questions. • What is the probability that you need to report towork on the 2mnd day (i.e., P(Day 2 = On Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you take a leave on the 2nd day (i.e., P(Day 2 = Off Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you go to work on the third day (i.e., P(Day 3=On Duty))? Answer: |(Please write your answer with 4 decimal points) • What is the probability that the third day was a Day Off (i.e., P(Day 3=Day Off)? Answer: (Please write your answer with 4 decimal points)

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6. A Markov chain has two non-absorbing states, A and B, and two absorbing states, C and D. Below are the one-cycle transition probabilities: from A to A: 10% from A to B: 20% O: 5000