3. The city of Mawroke maintains a constant voter population of 300,000 people per year. A political science study estimated that there were 150,000 Independents, 90,000 Democrats, and 60,000 Republicans in the city. It was also estimated that each year 20% of the Independents become Democrats and 10% become Republicans. Similarly, 20% of Democrats become Independents and 10% become Republicans, while 10% of Republicans defect to the Democrats and 10% become Independents each year.(a) Find the stochastic transition matrix $ A $ such that $ x^k = A x^{k-1} $, $ k = 1, 2, 3, \ldots $, where $ x^k $ is a vector representing the number of people in each group.(b) Find the eigenvalues of $ A $ and corresponding eigenvectors.(c) Factor $ A $ into a $ PDP^{-1} $, where $ D $ is diagonal.(d) Which group will dominate in the long run? Justify your answer by computing $ \lim_{n \to \infty} A^n x $.(Note: Above all, a blue stain or mark is present on the right side of the text.)

Answered: Image /qna-images/answer/5ae2917e-04f5-4e64-91b1-02bc2949e7f8.jpg

Answered: 3. The city of Mawroke maintains a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

In a small town there are 10,000 homes. When it comes to television viewing, the residents have three choices: they can subscribe to cable, they can pay for satellite service, or they watch no TV. (The town is sufficiently remote so that an antenna does not work.) In a given year, 80% of the cable customers stick with cable, 10% switch to satellite, and 10% quit watching TV. Over the same time period, 90% of satellite viewers continue with satellite service, 5% switch to cable, and 5% quit watching TV. And of those people who start the year not watching TV, 85% continue not watching, 5% subscribe to cable, and 10% get satellite service (see Figure below). Suppose that the current distribution is 8000 homes with cable, 1300 homes with satellite, and 700 homes with no TV. Find the distribution one year, two years, three years, and four years from now. (A graphing calculator is recommended. Round your answers to the nearest integer.) A = .80 .05 .05 .10 .90 .10 .10 .05 .85 cable satellite…
Business sensor technology provides a way for companies to learn about their customers, employees, and operations. A survey of global business and IT executives found that 26% of automotive executives; 27% of energy, utilities, and mining executives; 31% of hospitality and leisure executives; 31% of industrial products executives; and 51% of retail and consumer executives say their companies are currently investing in business sensor technology. Suppose these results were based on 400 business and IT executives in each of the five industries: Automotive; Energy, Utilities, and Mining; Hospitality and Leisure; Industrial Products; and Retail and Consumer. Complete parts (a) through (c). a. At the 0.05 level of significance, is there evidence of a difference among the industries with respect to the proportion of executives that say their companies are currently investing in business sensor technology? State the null and alternative hypotheses. A. Ho ₁₂ ====0 H₁: At least one of the лj is…
Suppose you try to conduct a presidential approval poll of 10,000 likely U.S. voters. You know that 44% of the voters are registered with the Independent party, 28% are registered with the Reform party and 23% are registered with the Green party. If you are going to construct a representative sample of this population, approximately how many of the likely voters in the sample should be Green party?
In a certain city, with a population of 1,000,000 people, 17 people have been infected with a disease. Five of these people are superspreaders. Superspreaders do not get sick, but will always be infected. Out of the remaining infected people, 50% do not get sick, and do not isolate, but will spread the disease for a week and then will no longer be infected. 35% will self-isolate and get better. The remaining 15% get sick and are admitted to hospital. Within a week, a superspreader will infect 0.1% of the population. A spreader is only infected for a week but will infect 0.01% of the population. Everyone in self-isolation will recover within a week. 50% of people in hospital will die, while the other 50% make a full recovery. a) Following this trend, what happens to the population over time?
Corporations and Elections. Based on research by the Associated Press and the National Constitution Center, 85% of Democrats, 81% of Republicans, and 78% of Independents support limiting corporate influence in political elections. Estimates from Gallup show that 32% of U.S. adults are Democrats, 28% are Republicans, and 40% are Independents. What percentage of U.S. adults who support limiting corporate influence in political elections are Republicans?
In a US presidential election, the incumbent president wins with 51.5% of the vote to 48.2% for the primary challenger (and .3% to others). In a nationwide telephone poll of 1000 people conducted exactly one week before the election by a university polling group, 49% of people polled supported the incumbent president, 50% supported the challenger, and 1% supported other candidates. a. For the polling study, what was the population of interest? b. What was the sample? c. Why did the sample results differ from the population? d. What are two constants that might have limited the generalizability of the polling results?
2. A liberal arts college has an endowment that pays engineering students a scholarship if they earn over a certain GPA in their junior year. There are three types of junior engineering students in the college: 40% are in chemical engineering, 25% are in electrical engineering and 35% are in mechanical engineering. It is known that both junior electrical and mechanical engineering students are twice as likely to earn the scholarship as junior chemical engineering students. If a chemical engineering student earns the scholarship they receive $2000 and if an electrical or mechanical engineering student earns the scholarship they receive $1000. Given that a junior engineering student earns a scholarship, find the expected amount that is paid to the student. Give answer to the fourth decimal.
In a clinical experiment, people newly diagnosed with depression were randomly placed into two treatment groups: group A only took medication to treat depression and group B took medication and also underwent counseling. They then tracked their progress and grouped results into two categories after one year of treatment: "good outcome" and "poor outcome" based on improvement from initial diagnosis. The results of this study are represented by the following contingency table: poor outcome good outcome medication & counseling medication only 24 276 42 258 Perform a relative risk analysis on this dataset. What is the relative risk score? (include three significant digits; e.g. 0.001)
A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.What is the probability that a randomly selected customer purchases the basic or classic car wash if they vacuum their car?A) 0.13B) 0.48C) 0.52D) 0.80
2.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS