Question 1

A state i is an absorbing state if pii = 0.

Accepted Answer

A) True 
 B)False

Question 2

If the probability of making a transition from a state is 0,then that state is called a(n)

Accepted Answer

A) steady state. 
B) final state. 
C) origin state. 
D) absorbing state. 
A) steady state. 
B) final state. 
C) origin state. 
D) absorbing state.

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

Steady state probabilities are independent of initial state.

Accepted Answer

A) True 
 B)False

Question 5

Explain the concept of memorylessness.

Accepted Answer

The concept of memorylessness refers to

Question 6

A television ratings company surveys 100 viewers on March 1 and April 1 to find what was being watched at 6:00 p.m.-- the local NBC affiliate's local news,the CBS affiliate's local news,or "Other" which includes all other channels and not watching TV.The results show   
a.What are the numbers in each choice for April 1?
b.What is the transition matrix?
c.What ratings percentages do you predict for May 1?

Accepted Answer

a.NBC 35,CBS 30,Othe

Question 7

A city is served by three cable TV companies: Xcellent Cable,Your Cable,and Zephyr Cable.A survey of 1000 cable subscribers shows this breakdown of customers from the beginning to the end of August. $$\begin{array} { c | c c c } 
\text { Company on } &  { \text { Company on August 31 } } \
\text { August 1 } & \text { Xcellent } & \text { Your } & \text { Zephyr } \
\hline \text { Xcellent } & 300 & 50 & 50 \
\text { Your } & 10 & 200 & 40 \
\text { Zephyr } & 40 & 80 & 230
\end{array}$$ 
a.Construct the transition matrix.
b.What was each company's share of the market at the beginning and the end of the month?
c.If the current trend continues what will the market shares be?

Accepted Answer

a.P = @#IMG-DLM& b.Market shares Aug 1 X

Question 8

Absorbing state probabilities are the same as

Accepted Answer

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

Question 9

A transition probability describes

Accepted Answer

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. 
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.

Question 10

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 52-inch LED televisions the shop stocks.   What is the probability that a customer who rented a TV this month will eventually buy it?

Accepted Answer

P(Buy)= .3

Question 11

The daily price of a farm commodity is up,down,or unchanged from the day before.Analysts predict that if the last price was down,there is a .5 probability the next will be down,and a .4 probability the price will be unchanged.If the last price was unchanged,there is a .35 probability it will be down and a .35 probability it will be up.For prices whose last movement was up,the probabilities of down,unchanged,and up are .1,.3,and .6.
a.Construct the matrix of transition probabilities.
b.Calculate the steady state probabilities.

Accepted Answer

a. @#IMG-DLM& b.F1F1F1S1F1F1F

Question 12

Two airlines offer conveniently scheduled flights to the airport nearest your corporate headquarters.Historically,flights have been scheduled as reflected in this transition matrix. $$\begin{array} { c | c c } 
\text { Current } &  { \text { Next Flight } } \
\text { Flight } & \text { Airline A } & \text { Airline B } \
\hline \text { Airline A } & .6 & .4 \
\text { Airline B } & .2 & .8
\end{array}$$ 
a.If your last flight was on B, what is the probability your next flight will be on A?
b.If your last flight was on B, what is the probability your second next flight will be on A?
c.What are the steady state probabilities?

Accepted Answer

a..2
b..28

Question 13

The probability of reaching an absorbing state is given by the

Accepted Answer

A) R matrix. 
B) NR matrix. 
C) Q matrix. 
D) (I F1F1F1S1F1F1F10 Q)F1F1F1S1F1F1F101 matrix 
A) R matrix. 
B) NR matrix. 
C) Q matrix. 
D) (I F1F1F1S1F1F1F10 Q)F1F1F1S1F1F1F101 matrix

Question 14

Joe Ferris,a stock trader at the brokerage firm of Smith,Jones,Johnson,and Thomas,Inc.has noticed that price changes in the shares of Dollar Department Stores at each trade are dependent upon the previous trade's price change.His observations can be summarized by the following transition matrix.   
a. What is the long-run average change in the value of a share of Dollar Department Stores' stock per trade?
b. If the shares of Dollar Department Stores are currently traded at $18 and the last trade was at 17 7/8, what is the probability the shares will sell at 18 in two trades?

Accepted Answer

a.Let, p₁ = the long-run probability of a

Question 15

A Markov chain cannot consist of all absorbing states.

Accepted Answer

A) True 
 B)False

A state i is an absorbing state if p_ii = 0.

If the probability of making a transition from a state is 0,then that state is called a(n)

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

Steady state probabilities are independent of initial state.

Explain the concept of memorylessness.

Absorbing state probabilities are the same as

A transition probability describes

The probability of reaching an absorbing state is given by the

A Markov chain cannot consist of all absorbing states.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility and Game Theory

Times Series Analysis and Forecasting

Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Filters

Exam 17: Markov Processes

A state i is an absorbing state if pii = 0.

If the probability of making a transition from a state is 0,then that state is called a(n)

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

Steady state probabilities are independent of initial state.

Explain the concept of memorylessness.

Absorbing state probabilities are the same as

A transition probability describes

The probability of reaching an absorbing state is given by the

A Markov chain cannot consist of all absorbing states.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility and Game Theory

Times Series Analysis and Forecasting

Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Filters

A state i is an absorbing state if p_ii = 0.