Exam 22: Markov Analysis

Markov analysis is a probabilistic technique.

Markov analysis is not an optimization technique.

The only car dealership in a community stocks cars from two manufacturers, Fret and Cessy. The following transition matrix shows the probabilities of a customer purchasing each brand of car in the next year given that he or she purchased that car in the current year. From / To Fret Cessy Fret .7 .3 Cessy .4 .6 Given that a customer purchased the brand Cessy in the present year (year 1), determine the probability that a customer will purchase Fret in year 3.

A Markov assumption is that the probabilities apply to all system participants.

A Markov assumption is that the probabilities change over time.

The only car dealership in a community stocks cars from two manufacturers, Fret and Cessy. The following transition matrix shows the probabilities of a customer purchasing each brand of car in the next year given that he or she purchased that car in the current year. From / To Fret Cessy Fret .7 .3 Cessy .4 .6 Given that a customer purchased the brand Fret in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3.

Decision trees can be used to solve for steady state probabilities.

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week. \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace Next Week This Week Don's Limmer's Don's 0.9 0.1 Limmer's 0.2 0.8 If a customer shopped at Don's the first week, what is the probability that they are shopping at Limmer's the third week?

Markov Analysis always results in a steady state.

A Markov assumption is that the probabilities in each row sum to 1 because they are mutually exclusive and collectively exhaustive.

A Markov process for two states has the following transition matrix: A 0.35 0.65 B 0.42 0.58 Assume that we start with state 1, what is the probability matrix of the system being in state A or B in period 3 given the system started in state B?

Markov analysis is a ________ technique.

For the following transition matrices, determine the transient or absorbing states. $\left| \begin{array} { l l l } .4 & 0 & .6 \\0 & .34 & .66 \\0 & .75 & .25\end{array} \right|$

Participants eligible for a retraining program can be in one of four states: A - not in the training program B - discharged C - in training D - employed You are given the following transition matrix and the fundamental matrix. B C D .1 .6 .3 0 0 1.0 0 0 .2 .2 .5 .1 0 0 0 1.0 1.28 0.77 0.51 2.31 Assume that there were initially 10 people not in the training program (State A) and 60 people who were in the training program (State C). Approximately how many people will be employed?

A Markov assumption is that the probabilities in each row sum to 1 because they are

The ________ is average, constant probability that the system will be in a state in the future.

Markov analysis is an optimization technique.

Steady state probabilities can be computed by developing a set of equations using ________ operations and solving them simultaneously.

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week. \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace Next Week This Week Don's Limmer's Don's 0.9 0.1 Limmer's 0.2 0.8 If there are 2000 customers who shop at either store, how many over the long run would shop at Limmer's?

________ probabilities are average constant probabilities that the system will be in a state in the future.