Deck 22: Markov Analysis

Question 1

If a Markov process contains an absorbing state, the process will eventually terminate in the absorbing state.

Answer 1

True

Question 2

Markov analysis is not an optimization technique.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

Markov analysis is a probabilistic technique.

Question 5

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

Question 6

A Markov assumption is that the probabilities are constant over time.

Question 7

Markov analysis is not a probabilistic technique.

Question 8

Markov analysis provides a recommended decision.

Question 9

Markov analysis can be used to determine the steady state probabilities associated with machine breakdowns.

Question 10

Markov Analysis always results in a steady state.

Question 11

A transition matrix cannot cause the system to cycle between states.

Question 12

Markov analysis does not provide a recommended decision.

Question 13

A Markov assumption is that the probabilities change over time.

Question 14

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

Question 15

The brand-switching problem analyzes the probability of customers' changing brands of a product over time.

Question 16

Markov analysis provides information on the probability of customers switching from one brand to one or more other brands.

Question 17

Markov analysis is a descriptive technique that results in probabilistic information.

Question 18

Markov analysis is not a descriptive technique that results in probabilistic information.

Question 19

Markov analysis is an optimization technique.

Question 20

The state of the system is where the system is at a point in time.

Question 21

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.
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.

Question 22

A ________ is the probability of moving from one state to another during one time period.

Question 23

A Markov process has the following transition matrix:
What are the steady state probabilities?

Question 24

Markov analysis is a ________ technique.

Question 25

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

Question 26

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.
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.

Question 27

A Markov process has the following transition matrix:
What are the steady state probabilities?

Question 28

In certain applications, the transition matrix may first need to be divided into submatrices. The identity matrix, I, and matrix Q (the nonabsorbing matrix) are then used to determine the ________ matrix.

Question 29

A common application of Markov analysis is ________.

Question 30

A Markov process has the following transition matrix:
What are the steady state probabilities?

Question 31

In Markov analysis, once the system leaves a(n) ________ state, it will never return.

Question 32

In Markov analysis, once the system moves into a(n) ________ state, it is trapped and cannot leave.

Question 33

A Markov process for two states has the following transition matrix:

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?

Question 34

Although information from Markov analysis can be obtained using a ________, it is time-consuming and cumbersome.

Question 35

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

Question 36

The probability of ending up in a state in the future is ________ of the starting state.

Question 37

An assumption of Markov analysis is that the probability of moving from a state to all other states sum to ________.

Question 38

A transition matrix is ________ when it moves back and forth between states.

Question 39

An assumption of Markov analysis is that the probabilities are ________ over time.

Question 40

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

Question 41

Limmer's is going to launch a new advertising campaign in order to attract new customers. The "before" and "after" transition matrices are shown below:
Before:
After:
If there are 1000 customers who shop at these two stores, how many customers, over the long run, will switch to Limmer's as a result of the new campaign?

Question 42

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.
Given that a customer purchased the brand Cessy in the present year (year 1), determine the probability that a customer will purchase Cessy in year 3.

Question 43

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

A) transition probability
B) state of the system
C) steady-state probability
D) transition matrix

Question 44

For the following transition matrices, what is the absorbing state(s)? $$\left| \begin{array} { l l l l } 0 & 0 & 2 / 3 & 1 / 3 \\0 & 1 & 0 & 0 \\3 / 4 & 1 / 4 & 0 & 0 \\1 & 0 & 0 & 0\end{array} \right|$$

A) state 1
B) state 2
C) state 3
D) state 4
E) state 2 and 4

Question 45

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

A) none of the
B) the major
C) some
D) all

Question 46

The ________ is the probability of moving from one state to another during one time period.

A) transition probability
B) state of the system
C) steady-state probabilities
D) transition matrix

Question 47

The ________ is where the system is at a point in time.

A) transition probability
B) state of the system
C) steady-state probabilities
D) transition matrix

Question 48

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

Question 49

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week. $$\begin{array}{l}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Next Week }\\\begin{array} { l c c } \text { This Week } & \text { Don's } & \text { Limmer's } \\\hline \text { Don's } & 0.9 & 0.1 \\\text { Limmer's } & 0.2 & 0.8\end{array}\end{array}$$ If a customer shopped at Don's the first week, what is the probability that they are shopping at Limmer's the third week?

A) 0.17
B) 0.34
C) 0.66
D) 0.83
E) none of the above

Question 50

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

A) mutually exclusive.
B) collectively exhaustive.
C) mutually exclusive and collectively exhaustive.
D) mutually exclusive or collectively exhaustive.

Question 51

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.

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). How many people will end up being discharged, and how many people will be employed?

Question 52

Markov analysis is a ________ technique that results in ________ information.

A) descriptive, descriptive
B) probabilistic, descriptive
C) descriptive, probabilistic
D) probabilistic, probabilistic

Question 53

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.
Determine the steady state probabilities for Fret and Cessy.

Question 54

A Markov assumption is that the probabilities ________ over time.

A) become smaller
B) become larger
C) change
D) are constant

Question 55

Markov analysis ________ a recommended decision.

A) does not provide
B) always provides
C) sometimes provides
D) rarely provides

Question 56

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
Given the following transition matrix, determine the fundamental matrix.

Question 57

For the following transition matrices, determine the transient or absorbing states.

Question 58

For the following transition matrices, determine the transient or absorbing states.

Question 59

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. $$\begin{array} { l c c c } \text { From } / & \text { To } & \text { Fret } & \text { Cessy } \\\hline \text { Fret } & & .7 & .3 \\\text { Cessy } & & .4 & .6 \\\hline\end{array}$$ 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.

A) .7
B) .61
C) .39
D) .21
E) .18

Question 60

Which of the following is not an assumption or a characteristic of a Markov Process?

A) The transition probabilities are the same for any customer.
B) The transition probabilities will remain constant over time.
C) The probability of being in a particular state at any one time period depends only on the state immediately preceding it.
D) In a transition matrix, sum of the row probabilities must sum to one.
E) In a transition matrix, sum of the column probabilities must sum to one.

Question 61

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. $$\begin{array} { r r r r r } & \mathrm { A } & { \text { B } } & \text { C } & \text { D } \\\hline \mathrm { A } & .1 & .6 & .3 & 0 \\\mathrm {~B} & 0 & 1.0 & 0 & 0 \\\mathrm { C } & .2 & .2 & .5 & .1 \\\mathrm { D } & 0 & 0 & 0 & 1.0\end{array}$$
$$\begin{array} { c c c } & \mathrm { A } & \mathrm { C } \\\hline \mathrm { A } & 1.28 & 0.77 \\\mathrm { C } & 0.51 & 2.31\end{array}$$
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) 10
B) 15
C) 40
D) 55
E) 60

Question 62

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. $$\begin{array} { l c c c } \text { From } / & \text { To } & \text { Fret } & \text { Cessy } \\\hline \text { Fret } & & .7 & .3 \\\text { Cessy } & & .4 & .6 \\\hline\end{array}$$ Determine the steady state probabilities for Fret and Cessy.

A) .875, .125
B) .645, .355
C) .621, .379
D) .571, .429
E).55, .45

Question 63

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. $$\begin{array} { r r r r r } & \mathrm { A } & { \text { B } } & \text { C } & \text { D } \\\hline \mathrm { A } & .1 & .6 & .3 & 0 \\\mathrm {~B} & 0 & 1.0 & 0 & 0 \\\mathrm { C } & .2 & .2 & .5 & .1 \\\mathrm { D } & 0 & 0 & 0 & 1.0\end{array}$$
$$\begin{array} { c c c } & \mathrm { A } & \mathrm { C } \\\hline \mathrm { A } & 1.28 & 0.77 \\\mathrm { C } & 0.51 & 2.31\end{array}$$
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 end up being discharged?

A) 10
B) 15
C) 40
D) 55
E) 60

Question 64

The transition matrix below shows the probabilities that customer switch between two grocery stores, Don's and Limmer's, each week. $$\begin{array}{l}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Next Week }\\\begin{array} { l c c } \text { This Week } & \text { Don's } & \text { Limmer's } \\\hline \text { Don's } & 0.9 & 0.1 \\\text { Limmer's } & 0.2 & 0.8\end{array}\end{array}$$ If there are 2000 customers who shop at either store, how many over the long run would shop at Limmer's?

A) 333
B) 400
C) 667
D) 1000
E) 1600