Exam 14: Markov Analysis

A state probability when equilibrium has been reached is called

In Markov analysis, the vector of state probabilities represents the market shares.

In Markov analysis, the likelihood that any system will change from one period to the next is revealed by the

If we are in any period n, we can compute the state probabilities for period n + 1 as π(n + 1)= π(n)P

A firm currently has a 20% market share for its product, lint pickers.It has identified 2 plans to improve its market share.The transition matrices for both plans are listed below.Plan 1 costs $1 million and Plan 2 costs $1.5 million.The company's goal is to determine what its demand will be in the long-term. A single percentage point of market share translates into an annual demand of 1,000 units per year.Also, each percentage point of market share means $100,000 of profit for the firm.Choose the plan that maximizes the firm's net income.

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 A two years from now?

There is a 30% chance that any current client of company A will switch to company B this year.There is a 40% chance that any client of company B will switch to company A this year.If these probabilities are stable over the years, and if company A has 500 clients and company B has 300 clients, (a)How many clients will each company have next year? (b)How many clients will each company have in two years?

In Markov analysis, the transition probability Pij represents the conditional probability of being in state i in the future given the current state of j.

A state that when entered, cannot be left is called

At equilibrium

The matrix of transition probabilities gives the conditional probabilities of moving from one state to another.

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 1's estimated popularity after students have taken the first introductory course.

A matrix of transition probabilities is of dimension P_mn.The vector of current market share must be of dimension π_m1.

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 steady state probability of the three diseases? P = π(0)= (.2, .3, .5)

Markov analysis assumes that there are a limited number of states in the system.

A certain firm has noticed that employees' salaries from year to year can be modeled by Markov analysis.The matrix of transition probabilities follows. (a)Set up the matrix of transition probabilities in the form: (b)Determine the fundamental matrix for this problem. (c)What is the probability that an employee who has received a raise will eventually quit? (d)What is the probability that an employee who has received a raise will eventually be fired?

Describe the situation of the existence of an equilibrium condition in a Markov analysis.

The state probabilities for n periods in the future can be obtained from the current state probabilities and the matrix of equilibrium probabilities.

"Events" are used to identify all possible conditions of a process or a system.

In Markov analysis, the row elements of the transition matrix must sum to 1.