# Quiz 16: Markov Processes

Business

Q 1Q 1

In Markov analysis, we are concerned with the probability that the
A) state is part of a system.
B) system is in a particular state at a given time.
C) time has reached a steady state.
D) transition will occur.

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Multiple Choice

B

Q 2Q 2

For a situation with weekly dining at either an Italian or Mexican restaurant,
A) the weekly visit is the trial and the restaurant is the state.
B) the weekly visit is the state and the restaurant is the trial.
C) the weekly visit is the trend and the restaurant is the transition.
D) the weekly visit is the transition and the restaurant is the trend.

Free

Multiple Choice

A

Q 3Q 3

A transition probability describes
A) the probability of a success in repeated, independent trials.
B) the probability a system in a particular state now will be in a specific state next period.
C) the probability of reaching an absorbing state.
D) None of the alternatives is correct.

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Multiple Choice

B

Q 4Q 4

The probability of going from state 1 in period 2 to state 4 in period 3 is
A) p

_{12}B) p_{23}C) p_{14}D) p_{43}Free

Multiple Choice

Q 5Q 5

The probability that a system is in a particular state after a large number of periods is
A) independent of the beginning state of the system.
B) dependent on the beginning state of the system.
C) equal to one half.
D) the same for every ending system.

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Multiple Choice

Q 6Q 6

At steady state
A)

_{1}(n+1) > _{1}(n) B) _{1}= _{2}C) _{1}+ _{2} 1 D) _{1}(n+1) = _{1}Free

Multiple Choice

Q 7Q 7

Analysis of a Markov process
A) describes future behavior of the system.
B) optimizes the system.
C) leads to higher order decision making.
D) All of the alternatives are true.

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Multiple Choice

Q 8Q 8

If the probability of making a transition from a state is 0, then that state is called a(n)
A) steady state.
B) final state.
C) origin state.
D) absorbing state.

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Multiple Choice

Q 9Q 9

Absorbing state probabilities are the same as
A) steady state probabilities.
B) transition probabilities.
C) fundamental probabilities.
D) None of the alternatives is true.

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Multiple Choice

Q 10Q 10

The probability of reaching an absorbing state is given by the
A) R matrix.
B) NR matrix.
C) Q matrix.
D) (I Q)

^{}^{1}matrixFree

Multiple Choice

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True False

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True False

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True False

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True False

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True False

Q 16Q 16

The fundamental matrix is used to calculate the probability of the process moving into each absorbing state.

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True False

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True False

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True False

Q 19Q 19

If an absorbing state exists, then the probability that a unit will ultimately move into the absorbing state is given by the steady state probability.

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True False

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True False

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True False

Q 22Q 22

A state i is a transient state if there exists a state j that is reachable from i, but the state i is not reachable from state j.

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True False

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True False

Q 24Q 24

When absorbing states are present, each row of the transition matrix corresponding to an absorbing state will have a single 1 and all other probabilities will be 0.

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True False

Q 25Q 25

For Markov processes having the memoryless property, the prior states of the system must be considered in order to predict the future behavior of the system.

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True False

Q 26Q 26

The sum of the probabilities in a transition matrix equals the number of rows in the matrix.

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True False

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True False

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True False

Q 29Q 29

If a Markov chain has at least one absorbing state, steady-state probabilities cannot be calculated.

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True False

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True False

Q 31Q 31

Rent-To-Keep rents household furnishings by the month. At the end of a rental month a customer can: a) rent the item for another month, b) buy the item, or c) return the item. The matrix below describes the month-to-month transition probabilities for 32-inch stereo televisions the shop stocks.
What is the probability that a customer who rented a TV this month will eventually buy it?

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Essay