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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 25–32, could the given matrix be the transition matrix of a Markov chain? [i 1 0
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist. A regular Markov chain with an absorbing state.
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist. An absorbing Markov chain that is regular.
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist.A regular Markov chain with two different stationary matrices.
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist.An absorbing Markov chain with two different stationary matrices.
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist.A Markov chain with no limiting matrix.
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist.A regular Markov chain with no limiting matrix.
In Problems 29–35, either give an example of a Markov chain with the indicated properties or explain why no such chain can exist.An absorbing Markov chain with no limiting matrix.
A company’s brand (X) has 20% of the market. A market research firm finds that if a person uses brand X, the probability is .7 that he or she will buy it next time. On the other hand, if a person
Table 1 gives the percentage of U.S. adults who at least occasionally used social networking sites in the given year. The following transition matrix P is proposed as a model for the data, where I
Recent technological advances have led to the development of four new milling machines: brand A, brand B, brand C, and brand D. Due to the extensive retooling and startup costs, once a company
The railroad in Problem 51 also has a fleet of tank cars. If 14% of the tank cars on the home tracks enter the national pool each month, and 26% of the tank cars in the national pool are returned to
In Problems 9–22, could the given matrix be the transition matrix of a regular Markov chain? .3 .7 L.2 .6
In Problems 9–22, could the given matrix be the transition matrix of a regular Markov chain? .5 .5 .8 .2
In Problems 9–22, could the given matrix be the transition matrix of a regular Markov chain? .3 .2 .7 .6
In Problems 9–22, could the given matrix be the transition matrix of a regular Markov chain? .2 0.8 00 1 .7 0.3
For each transition matrix P in Problems 23–30, solve the equation SP = S to find the stationary matrix S and the limiting matrix P̅. P = .1 .9 .6 .4
In Problems 31–36, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The n × n identity matrix is the transition matrix for a
In Problems 31–36, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The n × n matrix in which each entry equals 1/n is the
In Problems 31–36, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If the 2 x 2 matrix P is the transition matrix for a regular
In Problems 31–36, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If the 3 × 3 matrix P is the transition matrix for a regular
In Problems 31–36, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a transition matrix P for a Markov chain has a stationary
In Problems 31–36, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If P is the transition matrix for a Markov chain, then P has a
Acme Soap Company markets one brand of soap, called Standard Acme (SA), and Best Soap Company markets two brands, Standard Best (SB) and Deluxe Best (DB). Currently, Acme has 40% of the market, and
Most railroad cars are owned by individual railroad companies. When a car leaves its home railroad’s tracks, it becomes part of a national pool of cars and can be used by other railroads. The rules
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a Markov chain is regular, then it is absorbing.
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a Markov chain is absorbing, then it is regular.
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a Markov chain is absorbing, then it has a unique
In Problems 1–6, identify the absorbing states in the indicated transition matrix. A P = B с A .6 0 0 B .3 1 0 C .1 0 0
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If every state of a Markov chain is an absorbing state, then
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a Markov chain has exactly three states, one nonabsorbing
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly two states and at least one
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly three states, one absorbing
In Problems 41–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has an absorbing state, then it is an
Problems 9–16 refer to the following transition matrix: In Problems 9–12, find S1 for the indicated initial-state matrix S0 and interpret with a tree diagram.So = [1 0] P= А A A 1.8 в
Problems 9–16 refer to the following transition matrix: In Problems 9–12, find S1 for the indicated initial-state matrix S0 and interpret with a tree diagram.So = [0 1] P= А A A 1.8 в
Problems 9–16 refer to the following transition matrix: In Problems 9–12, find S1 for the indicated initial-state matrix S0 and interpret with a tree diagram.So = [.5 .5] P= А A A 1.8 в
Problems 9–16 refer to the following transition matrix: In Problems 9–12, find S1 for the indicated initial-state matrix S0 and interpret with a tree diagram.S0 = [.3 .7] P= А A A 1.8 в
In Problems 17–20, use the transition diagram to find S1 for the indicated initial-state matrix S0.S0 = [.2 .8] .7 A .3 .9 B Figure for Problems 17-24
In Problems 17–20, use the transition diagram to find S1 for the indicated initial-state matrix S0.S0 = [.6 .4] .7 A .3 .9 B Figure for Problems 17-24
In Problems 17–20, use the transition diagram to find S1 for the indicated initial-state matrix S0.S0 = [.7 .3] .7 A .3 .9 B Figure for Problems 17-24
In Problems 21–24, use the transition diagram to find S2 for the indicated initial-state matrix S0. So [.9 .1] .7 A .3 .9 B Figure for Problems 17-24
In Problems 21–24, use the transition diagram to find S2 for the indicated initial-state matrix S0.So = [.7 .3] .7 A .3 .9 B Figure for Problems 17-24
In Problems 25–32, could the given matrix be the transition matrix of a Markov chain? .9 1.4 .1 .8
Repeat Problem 63 if the initial-state matrix is S0 = [0 1].Data in Problem 63A Markov chain with two states has transition matrix P. If the initial-state matrix is So = [1 0], discuss the
In Problems 65–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If P is a transition matrix for a Markov chain, then the sum
In Problems 65–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If P is a transition matrix for a Markov chain, then the sum
In Problems 65–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If P is a transition matrix for a Markov chain, then the
In Problems 65–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If P is a transition matrix for a Markov chain, then the
In Problems 65–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If C is a state in the transition diagram for a Markov chain,
In Problems 65–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If C is a state in the transition diagram for a Markov chain,
The 2000 census reported that 41.9% of the households in the District of Columbia were homeowners and the remainder were renters. During the next decade, 15.3% of homeowners became renters, and the
The 2000 census reported that 66.4% of the households in Alaska were homeowners, and the remainder were renters. During the next decade, 37.2% of the homeowners became renters, and the rest continued
A drug has side effects for 60 out of 1,200 people in a test. What is the approximate empirical probability that a person using the drug will have side effects?
Find the probabilities in Problems 7–12 by referring to the tree diagram below. Start .6 4 M N .8 .2 .3 .7 -A B -А B
A spinning device has 5 numbers, 1, 2, 3, 4, and 5, each as likely to turn up as the other. A person pays $3 and then receives back the dollar amount corresponding to the number turning up on a
If the probability distribution for the random variable X is given in the table, what is the expected value of X? Xi Pi -3 .3 0 .5 4 .2
Find the probabilities in Problems 7–12 by referring to the tree diagram below. Start .6 4 M N .8 .2 .3 .7 -A B A B
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability that The card is an ace, given that it is a heart.
If the probability distribution for the random variable X is given in the table, what is the expected value of X? X Pi -2 .1 1 .2 0 .4 1 .2 2 .1
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is red, given that it is a face card.
Find the probabilities in Problems 7–12 by referring to the tree diagram below. Start .6 4 M N .8 .2 .3 .7 -A B A B
You draw and keep a single bill from a hat that contains a $5, $20, $50, and $100 bill. What is the expected value of the game to you?
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is a heart, given that it is an ace.
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is a face card, given that it is red.
You draw and keep a single coin from a bowl that contains 15 pennies, 10 dimes, and 25 quarters. What is the expected value of the game to you?
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is black, given that it is a club.
You draw and keep a single coin from a bowl that contains 120 nickels and 80 quarters. What is the expected value of the game to you?
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is a jack, given that it is red.
You draw a single card from a standard 52-card deck. If it is red, you win $50. Otherwise you get nothing. What is the expected value of the game to you?
Find the probabilities in Problems 13–16 by referring to the following Venn diagram and using Bayes’ formula (assume that the simple events in S are equally likely):P(U2 |R)
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is a club, given that it is black.
You draw a single card from a standard 52-card deck. If it is an ace, you win $104. Otherwise you get nothing. What is the expected value of the game to you?
Find the probabilities in Problems 13–16 by referring to the following Venn diagram and using Bayes’ formula (assume that the simple events in S are equally likely):P(U1 |R′)
A single card is drawn from a standard 52-card deck. In Problems 7–14, find the conditional probability thatThe card is red, given that it is a jack.
Find the probabilities in Problems 13–16 by referring to the following Venn diagram and using Bayes’ formula (assume that the simple events in S are equally likely):P(U2 |R′)
Find the probabilities in Problems 17–22 by referring to the following tree diagram and using Bayes’ formula. Round answers to three decimal places. P(U|C)
Find the probabilities in Problems 17–22 by referring to the following tree diagram and using Bayes’ formula. Round answers to three decimal places.
Answer Problems 18–25 using the following probability tree: P(A) Start .4 .6 A A' .2 .8 .3 .7 B B' - B B'
Find the probabilities in Problems 17–22 by referring to the following tree diagram and using Bayes’ formula. Round answers to three decimal places. P(W|C)
Find the probabilities in Problems 17–22 by referring to the following tree diagram and using Bayes’ formula. Round answers to three decimal places.
Find the probabilities in Problems 17–22 by referring to the following tree diagram and using Bayes’ formula. Round answers to three decimal places. P(V|C)
Answer Problems 18–25 using the following probability tree: Start .4 .6 A A'- .2 .8 .3 .7 B B' B B'
A card is drawn at random from a standard 52-card deck. Events G and H are G = the drawn card is black. H = the drawn card is divisible by 3 (face cards are not valued).
Answer Problems 18–25 using the following probability tree: Start .4 .6 A A'- .2 .8 .3 7 - B B' B B'
Find the probabilities in Problems 23–28 by referring to the following Venn diagram and using Bayes’ formula (assume that the simple events in S are equally likely):
Find the probabilities in Problems 23–28 by referring to the following Venn diagram and using Bayes’ formula (assume that the simple events in S are equally likely):
A friend offers the following game: She wins $1 from you if, on four rolls of a single die, a 6 turns up at least once; otherwise, you win $1 from her. What is the expected value of the game to you?
Answer Problems 18–25 using the following probability tree:P(A|B) Start .4 .6 A A'- .2 .8 .3 .7 B B' B B'
Find the probabilities in Problems 23–28 by referring to the following Venn diagram and using Bayes’ formula (assume that the simple events in S are equally likely):
A single die is rolled once. You win $5 if a 1 or 2 turns up and $10 if a 3, 4, or 5 turns up. How much should you lose if a 6 turns up in order for the game to be fair? Describe the steps you took
In Problems 27 and 28, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A 3-card hand is dealt from a standard deck. We are interested in the
In Problems 27 and 28, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain. A 3-card hand is dealt from a standard deck. We are interested in whether
In Problems 29 and 30, use the probabilities in the first tree diagram to find the probability of each branch of the second tree diagram. Start Start A A'- B B' 115 +15 لا
A card is drawn from a standard 52-card deck. If the card is a king, you win $10; otherwise, you lose $1. What is the expected value of the game?
In Problems 29 and 30, use the probabilities in the first tree diagram to find the probability of each branch of the second tree diagram. Start Start 113
A spinning device has 3 numbers, 2, 5, and 9, each as likely to turn up as the other. If the device is spun twice, what is the probability that (A) Two prime numbers are generated? (B) A larger
In a single draw from a standard 52-card deck, what are the probability and odds for drawing.(A) A jack or a queen? (B) A jack or a spade? (C) A card other than an ace?
A 5-card hand is dealt from a standard 52-card deck. If the hand contains at least one king, you win $10; otherwise, you lose $1. What is the expected value of the game?
(A) What are the odds for rolling a sum of 5 on the single roll of two fair dice? (B) If you bet $1 that a sum of 5 will turn up, what should the house pay (plus return your $1 bet) in order for the

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