[SOLVED] given the transition matrix P and initial-

> 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:

> 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 c

> 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? (

> Refer to Problem 63. The chemists at Acme Soap Company have developed a second new soap,Â called brand Y. Test-marketing this soap against the three established brands produces the following transitionÂ matrix: Proceed as in Proble

> Repeat Problems 61 if 40% of preferred customers are moved to the satisfactory category each year, and all other information remains the same. Data from Problem 61: An auto insurance company classifies its customers in three categories: poor, satisfacto

> 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 AP

> Find each indefinite integral and check the result by differentiating.

> 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 households that own their home. (A) Let S0 = 3.654 .3464 and find S1, S2, and S3

> The railroad in Problem 55 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

> The transition matrix for a Markov chain is Let mk denote the minimum entry in the third column of Pk . Note that m1 = .3. (A) Find m2, m3, m4, and m5 to three decimal places. (B) Explain why mk â¦ mk + 1 for all positive integers

> require the use of a graphing calculator. Refer to the transition matrix P in Problem 50. What matrix P do the powers of P appear to be approaching? Are the rows of P stationary matrices for P?

> The transition matrix for a Markov chain is (C) How many different stationary matrices does P have?

> Given the transition matrix (A) Discuss the behavior of the state matrices S1, S2, S3,c for the initial-state matrix S0 = [.2 .3 .5] . (B) Repeat part (A) for S0 = [1/3 1/3 1/3]. (C) Discuss the behavior of Pk

> Repeat Problem 45 if the red urn contains 5 red and 3 blue marbles, and the blue urn contains 1 red and 3 blue marbles. Data From Problem 45: A red urn contains 2 red marbles and 3 blue marbles, and a blue urn contains 1 red marble and 4 blue marbles. A

> approximate the stationary matrix S for eachÂ transition matrix P by computing powers of the transition matrix P. Round matrix entries to four decimal places

> 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 unique stationary matrix.

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The constant function g(x) = 5eπ is an antiderivative of itself.

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the 3 x 3 matrix P is the transition matrix for a regular Markov chain, then, at most, two of the entries of P are equal to 0

> 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 transition matrix for a regular Markov chain.

> refer to the regular Markov chain with transition matrix For calculate SP. Is S a stationary matrix? Explain.

> refer to the regular Markov chain with transition matrix For S = [.6 1.5], calculate SP. Is S a stationary matrix? Explain

> For each transition matrix P, solve the equation SP = S to find the stationary matrix S and the limiting matrix P.

> could the given matrix be the transition matrix of a regular Markov chain?

> Find each indefinite integral and check the result by differentiating.

> find a standard form for the absorbing Markov chain with the indicated transition diagram.

> could the given matrix be the transition matrix of a regular Markov chain?

> find the matrix product, if it is defined.

> 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 to be homeowners. Similarly, 71.5% of the renters beca

> Refer to Problem 93. 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

> 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 perf

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The constant function k(x) = 0 is an antiderivative of itself.

> 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 remainde

> A car rental agency has facilities at both JFK 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 ca

> Repeat Problem 85 if the probability of rain following a rainy day is .6 and the probability of rain following a nonrainy day is .1. Data from Problem 85: An outdoor restaurant in a summer resort closes only on rainy days. From past records, it is found

> Use a graphing calculator and the formula Sk = S0 Pk (Theorem 1) to compute the required state matrices. Find Pk for k = 2, 4, 8,c. Can you identify a matrix Q that the matrices Pk are approaching? If so, how is Q related to the results you discovered in

> Use a graphing calculator and the formula Sk = S0 Pk (Theorem 1) to compute the required state matrices. Data from Problem 81: (A) If S0 = 30 14, find S2, S4, S8,c. Can you identify a stateÂ matrix S that the matrices Sk seem to be approachin

> Show that if are probability matrices, then SP is a probability matrix.

> Repeat Problem 77 for the transition matrix A matrix is called a probability matrix if all its entries are real numbers between 0 and 1, inclusive, and the sum of the entries in each row is 1. So transition matrices are square probability matrices and

> Repeat Problem 75 if the initial-state matrix is S0 = [0 1] Data from Problem 75: A Markov chain with two states has transition matrix P. If the initial-state matrix is S0 = [1 0], discuss the relationship between the entries in the kth-state matrix and

> given the transition matrix P and initial-state matrix S0, find P4 and use P4 to find S4.

> Find each indefinite integral and check the result by differentiating.

> refer to the following transition matrix P and its powers: Using a graphing calculator to compute powers of P, find the smallest positive integer n such that the corresponding entries in Pn and Pn + 1 are equal when rounded to three decimal places.

> refer to the following transition matrix P and its powers: Find S3 for S0 = [1 0 0] and explain what it represents.

> refer to the following transition matrix P and its powers: Find S2 for S0 = [0 1 0] and explain what it represents.

> refer to the following transition matrix P and its powers: Find the probability of going from state B to state B in three trials.

> refer to the following transition matrix P and its powers: Find the probability of going from state B to state C in two trials.

> use the given information to draw the transition diagram and find the transition matrix. A Markov chain has three states, A, B, and C. The probability of going from state A to state B in one trial is 1. The probability of going from state B to state A in

> use the given information to draw the transition diagram and find the transition matrix. A Markov chain has two states, A and B. The probability of going from state A to state A in one trial is .6, and the probability of going from state B to state B in

> are there unique values of a, b, and c that make P a transition matrix? If so, complete the transition matrixÂ and draw the corresponding transition diagram. If not, explain why.

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The constant function k(x) = 0 is an antiderivative of the constant function (x) = p.

> is there a unique way of filling in the missing probabilities in the transition diagram? If so, complete the transition diagram and write the corresponding transition matrix. If not, explain why.

> Could the given matrix be the transition matrix of a Markov chain?

> Find the transition diagram that corresponds to the transition matrix of Problem 21. Matrix of Problem 21:

> Find the transition matrix that corresponds to the transition diagram of Problem 15. Diagram from Problem 15:

> use the transition diagram to find S1 and S2 for the indicated initial state matrix S0.

> Find each indefinite integral and check the result by differentiating.

> use the transition diagram to find S1 and S2 for the indicated initial state matrix S0.

> use the transition matrix to find S1 and S2 for the indicated initial state matrix S0.

> Use the transition diagram To find S1 and S2 for the indicated initial state matrix S0.

> Use the transition matrix find S1 and S2 for the indicated initial state matrix S0.

> Is F(x) = (ex – 10)(ex + 10) an antiderivative of ( (x) = 2e2x ? Explain.

> Use the transition matrix find S1 and S2 for the indicated initial state matrix S0.

> graph the region R bounded by the graphs of the equations. Use set notation and double inequalities to describe R as a regular x region and a regular y region and as a regular x region or a regular y region, whichever is simpler.

> graph the region R bounded by the graphs of the equations. Use set notation and double inequalities to describe R as a regular x region and a regular y region.

> evaluate each iterated integral.

> Repeat Problem 57 for the region bounded by y = 0 and y = 5 - 0.2x2 . Data from Problem 57: An industrial plant is located on the lakefront of a city. Let (0, 0) be the coordinates of the plant. The city's residents live in the region R bounded by y = 0

> The floor of a concert hall is the region bounded by x = 0 and x = 100 - 0.04y2. The ceiling lies on the graph of ((x, y) = 50 - 0.0025x2 . (Each unit on the x, y, and z axes represents one foot.) Find the volume of the concert hall (in cubic feet). The

> The floor of an art museum gallery is the region bounded by x = 0, x = 40, y = 0, and y = 50 - 0.3x. The ceiling lies on the graph of ((x, y) = 25 - 0.125x. (Each unit on the x, y, and z axes represents one foot.) Find the volume of the atrium (in cubic

> use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate th

> Find each indefinite integral and check the result by differentiating.

> use a graphing calculator to graph the region R bounded by the graphs of the indicated equations. Use approximation techniques to find intersection points correct to two decimal places. Describe R in set notation with double inequalities, and evaluate th

> reverse the order of integration for each integral. Evaluate the integral with the order reversed. Do not attempt to evaluate the integral in the original form.

> find the volume of the solid under the graph of ((x, y) over the region R bounded by the graphs of the indicated equations. Sketch the region R; the solid does not have to be sketched.

Question: given the transition matrix P and initial-