Question: approximate the stationary matrix S for each
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
> find each indefinite integral
> Find each indefinite integral and check the result by differentiating.
> Find the equation of the curve that passes through (1, 3) if its slope is given by for each x.
> Find each indefinite integral and check the result by differentiating.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Find each indefinite integral and check the result by differentiating.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Is F(x) = ln 1ln x2 an antiderivative of ? Explain.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Is F(x) = 1 - 0.2e-5x an antiderivative of (x) = e-5x Explain.
> find a standard form for the absorbing Markov chain with the indicated transition matrix.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Is F(x) = (x2 – 1)100 an antiderivative of (x) = 200x (x2 – 1)99? Explain.
> Find each indefinite integral. (Check by differentiation.)
> Is F(x) = 1/x an antiderivative of (x) = ln x? Explain.
> Find each indefinite integral. (Check by differentiation.)
> the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
> Find each indefinite integral. (Check by differentiation.)
> The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
> Find each indefinite integral. (Check by differentiation.)
> the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
> find a standard form for the absorbing Markov chain with the indicated transition diagram.
> Find each indefinite integral. (Check by differentiation.)
> Find each indefinite integral and check the result by differentiating.
> Find each indefinite integral. (Check by differentiation.)
> Find each indefinite integral and check the result by differentiating.
> Could the three graphs in each figure be anti-derivatives of the same function? Explain
> Find each indefinite integral and check the result by differentiating.
> could the given matrix be the transition matrix of a regular Markov chain?
> could the given matrix be the transition matrix of a regular Markov chain?
> Could the three graphs in each figure be anti-derivatives of the same function? Explain
> without using a calculator, find P100. [Hint: First find P2 .]
> without using a calculator, find P100. [Hint: First find P2.]
> without using a calculator, find P100. [Hint: First find P2 .]
> without using a calculator, find P100. [Hint: First find P2 .]
> 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, called brand Y. Test-marketing this soap against the three established brands produces the following transition 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 … 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 each 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.
> For each transition matrix P, solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
> For each transition matrix P, solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
> 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?
> 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?
> could the given matrix be the transition matrix of a regular Markov chain?
> could the given matrix be the transition matrix of a regular Markov chain?
> find the matrix product, if it is defined.
> find the matrix product, if it is defined.
> find the matrix product, if it is defined.
> 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 state 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.
> 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 matrix and draw the corresponding transition diagram. If not, explain why.
> are there unique values of a, b, and c that make P a transition matrix? If so, complete the transition matrix and draw the corresponding transition diagram. If not, explain why.
> are there unique values of a, b, and c that make P a transition matrix? If so, complete the transition matrix 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.
> 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.
> 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.
