Exam 15: Markov Analysis

One of the problems with using the Markov model to study population shifts is that we must assume that the reasons for moving from one state to another remain the same over time.

Table 15-2 The following data consists of a matrix of transition probabilities (P) of three competing retailers, the initial market share π(0). Assume that each state represents a retailer (Retailer 1, Retailer 2, Retailer 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 given in Table 15-2, find the market shares for the three retailers in month 1.

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 65% chance it will be sunny today. If it was raining yesterday, there is a 30% chance it will be sunny today. If the probability that it was raining yesterday is 0.4, what is the probability that it will be sunny today?

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

Three fast food hamburger restaurants are competing for the college lunch crowd. Burger Bills has 40% of the market while Hungry Heifer and Salty Sams each have 30% of the market. Burger Bills loses 10 % of its customers to Hungry Heifer and 10% to Salty Sams each month. Hungry Heifer loses 5% of its customers to Burger Bills and 10% to Salty Sams each month. Salty Sams loses 10% of its customers to Burger Bills while 20% go to Hungry Heifer. What will the market shares be for the three businesses next month?

Given the following matrix of transition probabilities, find the equilibrium states.

The copy machine in an office is very unreliable. If it was working yesterday, there is an 80% chance it will work today. If it was not working yesterday, there is a 10% chance it will work today. If it is working today, what is the probability that it will be working 2 days from now?

In the matrix of transition probabilities, P_ij is the conditional probability of being in state i in the future, given the current state j.

There is a 60% chance that customer without a smart phone will buy one this year. There is a 95% chance that a customer with a smart phone will continue with a smart phone going into the next year. If 30% of target market currently own smart phones, what proportion of the target market is expected to own a smart phone next year?

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

An equilibrium condition exists if the state probabilities for a future period are the same as the state probabilities for a previous period.

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

A state probability when equilibrium has been reached is called

In a(n) ________ state, you cannot go to another state in the future.

Table 15-1 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 15-1, determine Company 1's estimated market share in the next period.

In Markov analysis, the fundamental matrix

If in an absorbing state, the probability of being in an absorbing state in the future is ________.

Which of the following is not an assumption of Markov processes?

In Markov analysis, initial-state probability values determine equilibrium conditions.

If we want to use Markov analysis to study market shares for competitive businesses,