Answered: 3. The population of U.S. cities,… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

See similar textbooks

Related questions

Question

3. The population of U.S. cities, suburbs, and nonmetro areas in 2022 are described by the following vector
Io (in units of one million), and the populations in the following vears re given by a Markov Chain with
the transition matrix P. Ref
Initial
populations
80
city
Xo =
175
suburb
52
nonmetro
(from)
suburb
city
nonmetro
(to)
0.96
0.01
0.015 city
P = 0.03
0.98
0.005
suburb
L0.01
0.01
0.98
nonmetro
Determine the long-term predictions for the populations of these regions, assuming no change in their total
population. [

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)
43.10. Permanent disability is modeled as a Markov chain with three states: healthy (state 0), disabled (state 1), and dead (state 2). You are given the following transition forces: 0.05 5 (1) = 0.10 r>5 (i) 4, =0.02 (iii) p,-0.02 Calculate the probability that a healthy person age x will be dead at age x +10.
A continuous-time Markov chain (CTMC) has three states (1, 2, 3}. The average time the process stays in states 1, 2, and 3 are 2.1, 13.6, and 3.5 seconds, respectively. The steady-state probability that this CTMC is in the second state ( TT, ) is
Construct a model of population flow between metropolitan and nonmetropolitan areas of the United States, given that their respective populations in 2012 were 255 million and 52 million. The probabilities are given by the matrix (from) (to) metro nonmetro [0.99 [0.01 0.02] metro 0.98 nonmetro Predict the population distributions of metropolitan and nonmetropolitan areas for the years 2013 through 2015 (in millions, to four decimal places). If a person was living in a metropolitan area in 2012, what is the probability that the person will still be living in a metropolitan area in 2015?
7. The following 4-state Markov model with constant intensities a, B and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, B.y) for these data and hence find the maximum likelihood estimates of a,ß and y.
A factory worker will quit with probability 1/2 during her first month, with probability 1/4 during her second month and with probability 1/8 after that. Whenever someone quits, their replacement will start at the beginning of the next month. Model the status of each position as a Markov chain with 3 states. Identify the states and transition matrix. Write down the system of equations determining the long-run proportions. Suppose there are 900 workers in the factory. Find the average number of the workers who have been there for more than 2 months.
7. Dolphin behavior (seen in HW5). The behavior of dolphins in the presence of tour boats in Patagonia, Argentina is studied in Dans et al. (2012). A Markov chain model is developed, with state space consisting of five primary dolphin activities (socializing, traveling, milling, feeding, and resting). The following transition matrix is obtained. /0.84 0.11 0.01 0.04 0.03 0.80 0.04 0.10 0.03 P = | 0.01 0.15 0.70 0.07 0.07 0.03 0.19 0.02 0.75 0.01 \0.03 0.09 0.05 0.83/ Use technology to find the long-term distribution of dolphin activity. b. using this result, predict what behavior is the most likely to be observe long-term a.
Consider a continuous time Markov chain with three states {0, 1, 2} and transitions rates as follows: q01 = 3, q12 = 5, q21 = 6, q10 = 4 and the remaining rates are zeros. Find the limiting probabilities for the chain.
A continuous-time Markov chain (CTMC) has the following Q = (gij) matrix (all rates are transition/second) 41 22 7 29 46 Q = (4ij) : 27 39 38 1 3 Given that the process is in state 2, the probability to move next to state 1 is Given that the process is in state 3, the probability to move next to any other state is 2.
ZD In Smalltown, 90% of all sunny days are followed by sunny days, and 80% of all cloudy days are followed by cloudy days. Use this information to model Smalltown's weather as a Markov chain.
A population is modeled with three larva, pupa and adult, and the resulting structured 0.6 population model transition matrix is 0.5 0.9 0.8 (a) Explain what this matrix says about the three states. (b) Starting with a population of (0, 30, 100), does the population stabilize, increase or decrease over time? If it stabilizes, to what distribution?

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS