The diagrams below show three Markov chains, where arrows indicate anon-zero transition probability.AMarkov Chain 1State 1State 2State 3BMarkov Chain 2State 1.State 2State 3State 4Markov Chain 3State 1State 2State whether each of the chains is:irreducible[3]periodic, giving the period.

It is given the three diagram's named as Markov chain 1 , Markov chain 2 and Markov chain 3. It is…

Answered: The diagrams below show three Markov…

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The diagrams below show three Markov chains, where arrows indicate a non-zero transition probability.

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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An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known:p3,2=0.35, p3, 3=0.25, p3,5=0.4p4,1=0.35, p4,3=0.4, p4,4=0.25p5,1=0.3, p5,2=0.2, p5,4=0.3, p5,5 = 0.2(a) Let T denote the transition matrix. Compute T3. Find the probability that if you start in state #3 you will be in state #5 after 3 steps. (b) Compute the matrix N = (I - Q)-1. Find the expected value for the number of steps prior to hitting an absorbing state if you start in state #3. (Hint: This will be the sum of one of the rows of N.) steps(c) Compute the matrix B = NR. Determine the probability that you eventually wind up in state #1 if you start in state #4.
Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced Beginner Elementary Intermediate English Upper-Intermediate 0.4 0.1 0.05 0.45 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 Quit 1 Advanced Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1,…
Long-Run Properties of Markov Chains The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst -believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition -matrix from past data. What are the steady-state market shares for the two major -breweries?
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?
A certain television show airs weekly. Each time it airs, its ratings are categorized as "high," "average," or "low," and transitions between these categorizations each week behave like a Markov chain. If the ratings are high this week, they will be high, average, or low next week with probabilities 40%, 10%, and 50% respectively. If the ratings are average this week, they will be high, average, or low next week with probabilities 60%, 20%, and 20% respectively. If the ratings are low this week, they will be high, average, or low next week with probabilities 70%, 20%, and 10% respectively. Write all answers as integers or decimals. If the ratings are average this week, what is the probability that they will be low two weeks from now? If the ratings are average the first week, what is the probability that they will be low the second week? If the ratings are low the first week, what is the probability that they will be high the third week?
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.
Central topic markov chains: Every summer the Yates de los Lagos owners association decides if its annual regatta will be held in June, July or August. If it takes place in June, the probability of good weather is ¾; and if these conditions exist, the regatta of the next year it will be done in June with probability 2/3, in July with probability 1/6 or in August with probability 1/6; but if there is bad weather, next year's regatta will take place in July or August with equal probabilities. If the competition is held in July, good and bad weather have equal probabilities; if there is good weather, the next year's regatta will be held in July; If there is bad weather, the next regatta will take place in August with probability of 2/3 or in June with probability of 1/3. If the regatta takes place in August, the probability of good weather is 2/5; and if there are good conditions atmospheric conditions, next year's regatta will take place in July or August, with equal probabilities; but…
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?
The figure above illustrates a continuous-time Markov process. Suppose the system is currently instate 2. After a small amount of time Δ, what is the probability that the system is in each state?
Consider a Markov chain in the set {1, 2, 3} with transition probabilities p12 = p23 = p31 = p, p13 = p32 = p21 = q = 1 − p, where 0 < p < 1. Determine whether the Markov chain is reversible.
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?
Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct