Data collected from selected major metropolitan areas in the eastern United States show that 2% of individuals living within the city limits move to the suburbs during a one-year period, while 3% of individuals living in the suburbs move to the city during a one-year period. Answer the followingquestions assuming that this process is modeled by a Markov process with two states: city and suburbs.(a) Prepare the matrix of transition probabilities.FromCitySuburbs 0.030.98Need Help?CityRead ItTo(b) Compute the steady-state probabilities. (Enter your probabilities as fractions.)Cityπ 1 = 2/3Suburbs π₂ = 2/3XXWatch It0.020.97(c) In a particular metropolitan area, 40% of the population lives in the city, and 60% of the population lives in the suburbs. What population changes do your steady-state probabilities project for this metropolitan area?The area will show increasein the city population and decrease ✔ ✓ in the suburb population.Suburbs

The 2% of individuals living within the city move to the suburbs and 3% of individuals living in the…

Answered: Data collected from selected major…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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can you please do part d and e , please provide explanations
Aileen, a Scottish spy, has three fake identities that she uses to get information. The process is really quite involved, but she uses a Markov chain process to make it more difficult for her Irish adversaries to track her: "Hope" (state 1), "Trixie"(state 2), and "Fiona" (state 3). The transition matrix is .5 .5 P = .2 .2 .6 .4 .1 .5 On the first observation, Aileen used "Trixie" as her identity. Which of the three fake identities is she most likely to have used on the third observation? O Hope and Fiona are equally likely O Hope and Trixie are equally likely Fiona О Норе O None of the others are correct O Trixie
Redo exercises 21 through 23 in section 8.2 of your textbook, about the three types of employment in a small town, using the following data:
Long-Run Properties of Markov Chains The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst -believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition -matrix from past data. What are the steady-state market shares for the two major -breweries?
At Suburban Community College, 40% of all business majors switched to another major the next semester, while the remaining 60% continued as business majors. Of all non-business majors, 20% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. (Let 1 = business majors, and 2 = non-business majors.) calculate the probability that a business major will no longer be a business major in two semesters' time.
Please help me answer this. Thank you.
Please solve
A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).
Answer the following questions.
A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another. Electricity 10.2 Natural Gas Fuel Oil Solar Energy Elec. Gas Oil 0.60 0.05 0.10 0.15 0.85 0.10 0.08 Solar 0 0.10 0.02 0.75 0.08 0.15 0.08 0.05 0.84 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.) X % what
At Suburban Community College, 30% of all business majors switched to another major the next semester, while the remaining 70% continued as business majors. Of all non-business majors, 10% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. HINT [See Example 1.] (Let 1 business majors, and 2 = non-business majors.) = Calculate the probability that a business major will no longer be a business major in two semesters' time.

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