Exam 14: Markov Analysis

The following data consists of a matrix of transition probabilities (P)of Accounting, Economics, Finance, and Management and the count of students in each major.Assume that each state represents a major and the transition probabilities represent changes from one major to the next after taking the introductory class in each discipline. P = π(0)= (600, 50, 200, 250) Determine the number of majors in each discipline once steady state has been achieved.

Markov analysis is a technique that deals with the probabilities of future occurrences by analyzing currently known probabilities.

The fax machine in an office is very unreliable.If it was working yesterday, there is an 90% chance it will work today.If it was not working yesterday, there is a 5% chance it will work today. (a)What is the probability that it is not working today, if it was not working yesterday? (b)If it was working yesterday, what is the probability that it is working today?

Table 14-6 The following data consists of a matrix of transition probabilities (P)of four majors in the College of Business, and the initial proportion of students in each major π(0).Assume that each state represents a major and the transition probabilities represent changes from one major to the next after taking the introductory class in each discipline. P = π(0)= (.4, .3, .2, .1) -Using the data in Table 14-6, determine Major 3's estimated popularity after students have taken the first two introductory courses.

Equilibrium state probabilities may be estimated by using Markov analysis for a large number of periods.

Table 14-4 Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3).A transition matrix, indicating the probability that a resident in one city will travel to another, is given below.Cuthbert's job is to schedule the required number of seats, one to each person making the trip (transition), on a daily basis. C F T Transition matrix: π(0)= [100, 100, 100] -Using the data given in Table 14-4, how many seats should Cuthbert schedule for travel from Chaos to Frenzy for tomorrow?

The following data consists of a matrix of transition probabilities (P)of three potential diseases, and the initial incidence of each disease π(0).Assume that each state represents a disease (Disease 1, Disease 2, Disease 3, respectively)and the transition probabilities represent changes from one checkup to the next.What is the incidence of the three diseases in the next period? P = π(0)= (.2, .3, .5)

The matrix that is needed to compute equilibrium conditions when absorbing states are involved is called a(n)

Given the following matrix of transition probabilities, write three equations that, when solved, will give the equilibrium state values. P =

Table 14-1 The following data consists of a matrix of transition probabilities (P)of three competing companies, and the initial market share π(0).Assume that each state represents a company (Company 1, Company 2, Company 3, respectively)and the transition probabilities represent changes from one month to the next. P = π(0)= (0.3, 0.6, 0.1) -Using the data in Table 14-1, determine Company 2's estimated market share in the next period.

A collection of all state probabilities for a given system at any given period of time is called the

The weather is becoming important to you since you would like to go on a picnic today.If it was sunny yesterday, there is a 70% chance it will be sunny today.If it was raining yesterday, there is a 30% chance it will be sunny today.What is the probability it will be rainy today, if it was sunny yesterday?

Table 14-3 The following data consists of a matrix of transition probabilities (P)of three office locations (A,B,C)within a large company and how employees shift from one location to the other from year to year.The company CEO would like to understand the movement of employees over time and the long-run proportion of employees in each location.Assume that there is always a total of 3000 employees. A B C P = π(0)= [1000, 1000, 1000) -Using the data given in Table 14-3, what is the long run number of employees expected in location C?

In Markov analysis it is assumed that states are both mutually exclusive and collectively exhaustive.

Table 14-4 Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3).A transition matrix, indicating the probability that a resident in one city will travel to another, is given below.Cuthbert's job is to schedule the required number of seats, one to each person making the trip (transition), on a daily basis. C F T Transition matrix: π(0)= [100, 100, 100] -Using the data given in Table 14-4, how many people can we expect to find in each city tomorrow evening?

Table 14-3 The following data consists of a matrix of transition probabilities (P)of three office locations (A,B,C)within a large company and how employees shift from one location to the other from year to year.The company CEO would like to understand the movement of employees over time and the long-run proportion of employees in each location.Assume that there is always a total of 3000 employees. A B C P = π(0)= [1000, 1000, 1000) -Using the data given in Table 14-3, how many employees do we expect in location B two years from now?

The vector of state probabilities gives the probability of being in particular states at a particular point in time.

Given the following vector of state probabilities and the accompanying matrix of transition probabilities, find the next period vector of state probabilities. (0.4 0.4 0.2)

Table 14-6 The following data consists of a matrix of transition probabilities (P)of four majors in the College of Business, and the initial proportion of students in each major π(0).Assume that each state represents a major and the transition probabilities represent changes from one major to the next after taking the introductory class in each discipline. P = π(0)= (.4, .3, .2, .1) -Using the data in Table 14-6, determine Major 2's estimated popularity after students have taken the first introductory course.

Table 14-5 The following data consists of a matrix of transition probabilities (P)of three potential diseases, and the initial incidence of each disease π(0).Assume that each state represents a disease (Disease 1, Disease 2, Disease 3, respectively)and the transition probabilities represent changes from one checkup to the next. P = π(0)= (.3, .3, .4) -Using the data in Table 14-5, determine Disease 1's estimated incidence in the next period.