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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
Repeat Problem 67 forProblem 67 The transition matrix for a Markov chain is (A)If S0 = [0 1], find S2, S4, S8,.... Can you identify a state matrix S that the matrices Skseem to be approaching? (B) Repeat part (A) for S0 = [1 0]. (C) Repeat part (A) for S0 = [.5 .5]. (D) Find SP for any matrix S you
Refer to Problem 68. Find Pk for k = 2,4, 8,... . Can you identify a matrix Q that the matrices Pk are approaching? If so, how is Q related to the results you discovered in Problem 68? Use a graphing calculator and the formula Sk = SQP k (Theorem 1) to compute the required state matrices in Problem
Repeat Problem 71 if the probability of rain following a rainy day is .6 and the probability of rain following a non rainy day is .1. Problem 71 An outdoor restaurant in a summer resort closes only on rainy days. From past records, it is found that from May through September, when it rains one day,
A car rental agency has facilities at both Kennedy and LaGuardia airports. Assume that a car rented at either airport must be returned to one or the other airport. If a car is rented at LaGuardia, the probability that it will be returned there is .8; if a car is rented at Kennedy, the probability
A small community has two heating services that offer annual service contracts for home heating: Alpine Heating and Badger Furnaces. Currently, 25% of homeowners have service contracts with Alpine, 30% have service contracts with Badger, and the remainder do not have service contracts. Both
All welders in a factory begin as apprentices. Every year the performance of each apprentice is reviewed. Past records indicate that after each review, 10% of the apprentices are promoted to professional welder, 20% are terminated for unsatisfactory performance, and the remainder continue as
In Problem find S2 for the indicated initial-state matrix S0, and explain what it represents.S0 = [.3 .7]Problem refer to the following transition matrix:
Refer to Problem 79. During the open enrollment period, university employees can switch between two available dental care programs: the low-option plan (LOP) and the high-option plan (HOP). Prior to the last open enrollment period, 40% of employees were enrolled in the LOP and 60% in the HOP.
The 1990 census reported that 58.4% of the households in Alaska were homeowners, and the remainder were renters. During the next decade, 2.1% of the homeowners became renters, and the rest continued to be homeowners. Similarly, 23.4% of the renters became homeowners, and the rest continued to
In Problem, could the given matrix be the transition matrix of a regular Markov chain?
In Problem, could the given matrix be the transition matrix of a regular Markov chain?
For each transition matrix P in Problem, solve the equation SP = S to find the stationary matrix S and the limiting matrix
For each transition matrix P in Problem, solve the equation SP = S to find the stationary matrix S and the limiting matrix
For each transition matrix P in Problem, solve the equation SP = S to find the stationary matrix S and the limiting matrix
For each transition matrix P in Problem, solve the equation SP = S to find the stationary matrix S and the limiting matrix
In Problem, approximate the stationary matrix S for each transition matrix P by computing powers of the transition matrix P. Round matrix entries to four decimal places.
In Problem, approximate the stationary matrix S for each transition matrix P by computing powers of the transition matrix P. Round matrix entries to four decimal places.
Repeat Problem 33 if the red urn contains 5 red and 3 blue marbles, and the blue urn contains 1 red and 3 blue marbles. Problem 33 A red urn contains 2 red marbles and 3 blue marbles, and a blue urn contains 1 red marble and 4 blue marbles. A marble is selected from an urn, the color is noted, and
Give the transition matrix(A) Discuss the behavior of the state matrices S1, S2,53,... for the initial-state matrix 50 = [.2 .3 .5]. (B) Repeat part (A) for S0 = [1/3 1/3 1/3 ]. (C) Discuss the behavior of Pk, k = 2, 3,4,... . (D) Which of the conclusions of Theorem 1 are not valid for this
The Matrix for a Markov chain is(A) Show that R = [.4 0 .6] and S = [0 1 0] are both stationary matrices for P. Explain why this does not contradict Theorem 1 A. (B) Find another stationary matrix for P. [Consider T = aR + (1 - a)S, where 0 (C) How many different stationary matrices does P have?
The transition matrix for a Markov chain isLet Mk denote the maximum entry in the second column of Pk. m1 = .3. (A) Find m2, m3, m4, and m5 to three decimal places. (B) Explain why Mk ‰¤ Mk+1 for all positive integers k.
The railroad in Problem 43 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 the home tracks each month, what percentage of its tank cars can the railroad expect to have on its
The U.S. Census Bureau published the home ownership rates given in Table 2.The following transition matrix P is proposed as a model for the data, where H represents the house holds that own their home. (A) Let S0 = [.433 .567], and find S1 , S2, and S3. Compute the matrices exactly and then round
Consumers in a certain area can choose between three package delivery services: APS, GX, and WWP. Each week, APS loses 10% of its customers to GX and 20% to WWP; GX loses 15% of its customers to APS and 10% to WWP; and WWP loses 5% of its customers to APS and 5% to GX. Assuming that these
Repeat Problem 49 if 40% of preferred customers are moved to the satisfactory category each year, and all other information remains the same. Problem 49 An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 40% of those in the poor
Problem require the use of a graphing calculator.Refer to Problem 51. The chemists at Acme Soap Company have developed a second new soap, called brand Y. Test-marketing this soap against the three established brands produces the following transition matrix:Proceed as in Problem 51 to approximate
Suppose that a gene in a chromosome is of type A or type B. Assume that the probability that a gene of type A will mutate to type B in one generation is 10"4 and that a gene of type B will mutate to type A is 10-6. (A) What is the transition matrix? (B) After many generations, what is the
The Senate is in the middle of a floor debate, and a filibuster is threatened. Senator Hanks, who is still vacillating, has a probability of .1 of changing his mind during the next 5 minutes. If this pattern continues for each 5 minutes that the debate continues, and if a 24-hour filibuster takes
Table 4 gives the percentage of the U.S. population living in the northeast region during the indicated years.The following transition matrix P is proposed as a model for the data, where N represents the population that lives in the northeast region: (A) Let S0 = [.241 .759] and find S1, S2, and
In Problem, could the given matrix be the transition matrix of a regular Markov chain?
In Problem, identify the absorbing states for each transition diagram, and determine whether or not the diagram represents an absorbing Markov chain.
In Problem, could the given matrix be the transition matrix of an absorbing Markov chain?
In Problem, could the given matrix be the transition matrix of an absorbing Markov chain?
In Problem, find a standard form for the absorbing Markov chain with the indicated transition matrix.
In Problem, find a standard form for the absorbing Markov chain with the indicated transition matrix.
In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each non absorbing state to each absorbing state and the average number of trials needed to go from each non absorbing state to an absorbing state.
In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each non absorbing state to each absorbing state and the average number of trials needed to go from each non absorbing state to an absorbing state.
In Problems 29-34, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each non absorbing state to each absorbing state and the average number of trials needed to go from each non absorbing state to an absorbing state.
For matrix P from Problem 30 with (A) S0 = [0 0 1] (B) S0 = [.2 .5 .3] Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated
For matrix P form problem 32 with (A) S0 =[0 0 1] (B) S0 - [.2 .5 .3] Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state matrices for the indicated
For matrix P from Problem 34 with(A) S0 = [000 1](B) S0 = [001 0](C) S0 = [00.4 .6](D) S0 = [.1.2 .3 .4]Problems 35-40 refer to the matrices in Problems 29-34. Use the limiting matrix P found for each transition matrix P in Problems 29-34 to determine the long-run behavior of the successive state
In Problem, use a graphing calculator to approximate the limiting matrix for the indicated standard form.
In Problem, use a graphing calculator to approximate the limiting matrix for the indicated standard form.
Repeat Problem 53 forProblem 53 The following matrix P is a nonstandard transition matrix for an absorbing Markov chain: To find a limiting matrix for P, follow the steps outlined below. Step 1 Using a transition diagram, rearrange the columns and rows of P to produce a standard form for this
Verify the results in Problem 54 by computing Pk on a graphing calculator for large values of k.
. Show that S = [x 1 - x 0 0], 0 ‰¤ x ‰¤ 1, is a stationary matrix for the transition matrixDiscuss the generalization of this result to any absorbing Markov chain with two absorbing states and two absorbing states.
Refer to the matrices P and Q of Problem 59. For k a positive integer, let Tk = I + Q + Q2 + ˆ™ ˆ™ ˆ™ + Qk.(A) Explain why Tk+1 = TkQ + I.(B) Using a graphing calculator and part (A) to quickly compute the matrices Tk, discover and describe the connection between (I -
A chain of car muffler and brake repair shops maintains a training program for its mechanics. All new mechanics begin training in muffler repairs. Every 3 months, the performance of each mechanic is reviewed. Past records indicate that after each quarterly review, 30% of the muffler repair trainees
Once a year company employees are given the opportunity to join one of three pension plans: A,B.or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 4% of employees elect to join plan A,14% elect
The study discussed in Problem 65 also produced the following data for patients who underwent aortic valve replacements: each day 2% of the patients in the ICU died, 60% were transferred to the CCW, and the remainder stayed in the ICU. Furthermore, each day 5% of the patients in the CCW developed
Repeat Problem 67 if the exit from room B to room R isProblem 67A rat is placed in room for room B of the maze shown in the figure. The rat wanders from room to room until it enters one of the rooms containing food, L or R. Assume that the rat chooses an exit from a room at random and that once it
In Problem, use the graph of the function g shown to estimate the indicated limits and function values.(A) (B) (C) (D) f(2)
In Problem, use the graph of the function g shown to estimate the indicated limits and function values.(A) (B) (C) (D) f(4)
In Problem, use the graph of the function f shown to estimate the indicated limits and function values.(A) (B) (C) (D) f(-2) (E) is it possible to redefine f(-2) so that Explain.
In Problem, use the graph of the function f shown to estimate the indicated limits and function values.(A) (B) (C) (D) f(2) (E) is it possible to redefine f(2) so that Explain.
Given thatAnd Find the indicated limits in Problem.
Given thatAnd Find the indicated limits in Problem.
In Problem, sketch a possible graph of a function that satisfies the given conditions.
In Problem, sketch a possible graph of a function that satisfies the given conditions.
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C) (D) f(-1)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C) (D) f(-2)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C) (D) f(3)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C)
In Problem, find each indicated quantity if it exists.LetFind (A) (B) (C)
In Problem, use the graph of the function f shown to estimate the indicated limits and function values.(A) (B) (C) (D) f(1)
Compute the following limit for each function in Problem.f(x) = 5x - 1
Compute the following limit for each function in Problem.f(x) = x2 - 2
Let f be defined byWhere m is a constant. (A) Graph f for m = 0, and find (B) Graph f for m = 1, and find (C) Find m so that and graph f for this value of m. (D) Write a brief verbal description of each graph. How does the graph in part (C) differ from the graphs in parts (A) and (B)?
Find each limit in Problem, where a is a real constant.
Find each limit in Problem, where a is a real constant.
A second long-distance telephone service charges $0.09 per minute or fraction thereof for calls lasting 10 minutes or more and $0.18 per minute or fraction thereof for calls lasting less than 10 minutes.(A) Write a piecewise definition of the charge G(x) for a long-distance call lasting x
Refer to Problem 75. Write a brief verbal comparison of the two services described for calls lasting more than 20 minutes.Problem 75A long-distance telephone service charges $0.99 for the first 20 minutes or less of a call and $0.07 per minute for each additional minute or fraction thereof.(A)
In Problem, use the graph of the function g shown to estimate the indicated limits and function values.g (2.5)
Assume that the volume discounts in Table 1 apply only to that portion of the volume in each interval. That is, the discounted price for a $4,000 purchase would be computed as follows: 300 + 0.97(700) + 0.95(2,000) + 0.93(1,000) = 3,809 (A) If x is the volume of a purchase before the discount is
Refer to Problem 81. The fee per ton of pollution is given by A(x) = F(x)/x. Write a piecewise definition of A(x). What is the limit of A(x) as x approaches 4,000 tons? As x approaches 8,000 tons? Problem 81 A state charges polluters an annual fee of $20 per ton for each ton of pollutant emitted
In Problem, find each limit. Use -ˆž and ˆž when appropriate.(A) (B) (C)
In Problem, find each limit. Use -ˆž and ˆž when appropriate.(A) (B) (C)
In Problem, find each limit. Use -ˆž and ˆž when appropriate.(A) (B) (C)
In Problem, find each limit. Use -ˆž and ˆž when appropriate.(A) (B) (C)
In Problem, find the limit of each polynomial p(x) (A) As x approaches ∞ (B) As x approaches - ∞ p(x) = 4x3 - 3x4 + x2.
In Problem, find the limit of each polynomial p(x) (A) As x approaches ∞ (B) As x approaches - ∞ p(x) = 2x4 - 2x3 +9x
In Problem, use -ˆž or ˆž where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes
In Problem, use -ˆž or ˆž where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.
In Problem, use -ˆž or ˆž where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.
In Problem, use -ˆž or ˆž where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.
In Problem, find each function value and limit. Use -ˆž or ˆž where appropriate.(A) f(5) (B) f(10) (C)
In Problem, find each function value and limit. Use -ˆž or ˆž where appropriate.(A) f(8) (B) f(16) (C)
In Problem, find each function value and limit. Use -ˆž or ˆž where appropriate.(A) f(-10) (B) f(-20) (C)
In Problem, find each function value and limit. Use -ˆž or ˆž where appropriate.(A) f(-50) (B) f(-100) (C)
In Problem, find all horizontal and vertical asymptotes.
In Problem, find all horizontal and vertical asymptotes.
In Problem, find all horizontal and vertical asymptotes.
In Problem, find all horizontal and vertical asymptotes.
In Problem, find all horizontal and vertical asymptotes.
In Problem, find all horizontal and vertical asymptotes.
In Problem, find all horizontal and vertical asymptotes.
Theorem 3 also states thatWhat conditions must n and an satisfy for the limit to be ˆž? For the limit to be - ˆž?
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