A state condition where-as the probability of one event changes as a result of occurrence

Question 1

A state condition where-as the probability of one event changes as a result of occurrence of another related event is known as:

[removed]	1.	initial probability
[removed]	2.	transition matrix
[removed]	3.	stationary probability
[removed]	4.	conditional probability

5 points

Question 2

The steady state probabilities of a double stochastic probability matrix is equal to

[removed]	1.	1.0
[removed]	2.	1/(m*n), where m is the number of rows of the matrix and n is the number of columns of the matrix
[removed]	3.	1/n, where n is the number of columns in the matrix
[removed]	4.	0.50
[removed]	5.	None of the above

6 points

Question 3

The Markov state where, in all conditions, it will never converge to steady state is

[removed]	1.	Periodic State
[removed]	2.	Absorbing State
[removed]	3.	Ergodic State
[removed]	4.	Trapping State
[removed]	5.	Transient

6 points

Question 4

Match the term with the associtated definition

Stochastic Process

	Time

	State

Transition

A.	A vector that describes attributes of a system at any point in time.
B.	The parameter of a stochastic process.
C.	A random variable, {X(t)}, where t is a time index that takes values from a given set T. T may be discrete or continuous
D.	A function that determines the next state, s', based on the current state, s, and the event, x. Also known as the Transition Matrix

12 points

Question 5

Steady State Probability of Markov Chains are

[removed]	1.	States of condition that reach probability value equal to 1.0 in all cases
[removed]	2.	Is the convergence to an equilibrium or “steady state” condition and applies to all markov chains
[removed]	3.	Steady State Probabilities is the product of Steady State Probabilities multiplied by the Transition Matrix
[removed]	4.	All of the above
[removed]	5.	None of the above

6 points

Question 6

A Transition matrix is

[removed]	1.	Current states of a system at time t
[removed]	2.	Conditional probabilities that involve moving from one state to another
[removed]	3.	The stationary assumption of a markov chain
[removed]	4.	A m by n matrix of probabilities
[removed]	5.	none of the above

6 points

Question 7

In a transition matrix where the sum probabilities values in each column equals 1.0 is referred to as

[removed]	1.	Steady State Probabilities
[removed]	2.	Conditional Probability Matrix
[removed]	3.	Stationary Matrix
[removed]	4.	Double Stochastic Transition Matrix
[removed]	5.	None of the above

6 points

Question 8

Which of the following is true regarding the markov Analysis Methodology

[removed]	1.	States of Nature are outcomes of a process (machine operating or broken, % of customers buying product A & B, etc)
[removed]	2.	There exist an initial probability associated with the state of nature (100% operational and 0% broken, 80% customers buy product A and 20% buy product B)
[removed]	3.	There is also transition (or conditional) probabilities of moving from one state to another (represented by the Transition Matrix)
[removed]	4.	All of the above
[removed]	5.	None of the above

6 points

Question 9

A Markov Chain is

[removed]	1.	A discrete-time stochastic process that is a description of the relation between the random variables at various states (in time) X0, X1, X2
[removed]	2.	A continuous –time stochastic process in which the state of the system can be viewed at any time, not just at discrete instants in time.
[removed]	3.	A probability assessment that is not conditional
[removed]	4.	All of the above
[removed]	5.	None of the above

6 points

Question 10

Match the state classification to the appropriate term

communicate

	absorbing

	transient

	recurrent

ergodic

A.	state (j) is reachable from state (i) and vice versa
B.	a state that is not transient
C.	state (j) is reachable from (i), but state (i) is not reachable from state (j)
D.	all states in the cahin are recurrent, aperiodic and communicate with each other
E.	steady state probability value equal to 1.0

12 points

Question 11

This condition where the probability relating the next period’s state to the current state does not change over time is referred to as

[removed]	1.	Transition Matrix
[removed]	2.	Stationary Assumption
[removed]	3.	Marvov Process
[removed]	4.	Markov Chain
[removed]	5.	Initial Probability Distribution

6 points

Question 12

A process where-by the input variables are random and are defined by distributions rather than a single number is known as a

[removed]	1.	Markov Process
[removed]	2.	Stochastic Process
[removed]	3.	Deterministic Process
[removed]	4.	All of the above
[removed]	5.	None of the above

6 points

Question 13

Which of the following is a true statement regarding Markov Analysis

[removed]	1.	Markov Analysis is a Technique that involves predicting probabilities of future occurrences
[removed]	2.	Markov Analysis is a stochastic process in which current states of a system depend on previous states
[removed]	3.	The objective of Markov Analysis is to predict future states of nature given the probabilities of existing states
[removed]	4.	All of the above are true regarding Markov Analysis
[removed]	5.	All of the above are NOT true regarding Markov Analysis

6 points

Question 14

Which of the following are Markov properties

[removed]	1.	The states of nature are mutually exclusive and collectively exhausted
[removed]	2.	Each entry in the transition matrix is a conditional probability that is nonnegative in value
[removed]	3.	The summation of all the probabilities in the transition matrix sume to a value of 1.0 along each row in the matrix
[removed]	4.	All of the above
[removed]	5.	None of the above

5 points

Question 15

The Markov state that is characterized by all zero’s in the retention cells (diagonal of the matrix) and all one’s or zero’s in non retention cells is referred to as

[removed]	1.	Periodic State
[removed]	2.	Absorbing State
[removed]	3.	Trapping State
[removed]	4.	Ergodic State
[removed]	5.	Transient

6 points

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