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 following questions assunthat this process is modeled by a Markov process with two states: city and suburbs.(a) Prepare the matrix of transition probabilities.FromCitySuburbsCityToSuburbs(b) Compute the steady-state probabilities. (Enter your probabilities as fractions.)CityT₁ =Suburbs T₂ =(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 ---Select--- in the city population and --Select-- in the suburb population.

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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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:
Profits at a securities firm are determined by the volume of securities sold, and this volume fluctuates from week to week. If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. If volume is low this week then it will be high next week with a probability of 0.1. 1. Find the transition matrix for the Markov chain, with high volume being state 1 and low volume state 2. 2. If the volume was low last week, what is the probability the volume will be low this week? 3. If the volume was high this week, what is the probability it will be low three weeks from now? 4. If the volume was high this week, what is the probability it will be alternate between low and high for the next three weeks (i.e. High → Low → High → Low.)
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?
A certain television show airs weekly. Each time it airs, its ratings are categorized as "high," "average," or "low," and transitions between these categorizations each week behave like a Markov chain. If the ratings are high this week, they will be high, average, or low next week with probabilities 40%, 10%, and 50% respectively. If the ratings are average this week, they will be high, average, or low next week with probabilities 60%, 20%, and 20% respectively. If the ratings are low this week, they will be high, average, or low next week with probabilities 70%, 20%, and 10% respectively. Write all answers as integers or decimals. If the ratings are average this week, what is the probability that they will be low two weeks from now? If the ratings are average the first week, what is the probability that they will be low the second week? If the ratings are low the first week, what is the probability that they will be high the third week?
Can someone please help me with this question. I am having so much trouble.
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.
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The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?
The Tiger Sports Shop1 has hired you as an analyst to understand its market position with respect to Clemson merchandise. It is particularly concerned about its major competitor, Mr. Knickerbocker, and which Clemson-related store has the ‘lead’ market share. Recent history has suggested that which Clemson-related store has the ‘lead market share’ can be modeled as a Markov Chain using three states: TSS (Tiger Sports Shop), MK (Mr. Knickerbocker), and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data in the picture. a) The current state of the lead market share in October is that Tiger Sports Shop is in the lead (i.e., the Markov Chain in October is TSS). Tiger Sports Shop is considering launching a new brand in February only if it has the lead market share in January. Determine the probability that TSS will launch this new brand. Please show any equations or matrices…
We will use Markov chain to model weather XYZ city. According to the city’s meteorologist, every day in XYZ is either sunny, cloudy or rainy. The meteorologist have informed us that the city never has two consecutive sunny days. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next possibilities. In the long run, what proportion of days are cloudy, sunny and rainy? Show the transition matrix.
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