In a large metropolitan area, 15% of the commuters currently use the public transportation system, whereas the remaining 85% commute via automobile. The city has recently revitalized and expanded its public transportation system.It is expected that 6 months from now 10% of those who are now commuting to work via automobile will switch to public transportation, and 90% will continue to commute via automobile. At the same time, it is expected that 20% ofthose now using public transportation will commute via automobile and 80% will continue to use public transportation.(a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters.PT =A(b) Find the initial distribution vector for this Markov chain.Xo =(c) What percentage of the commuters are expected to use public transportation 6 months from now? (Round your answer to the nearest percent.)

Answered: a, 15% of the commuters currently use…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Show full answers and steps to this exercise. Please explain how you get to the answers using Markov Chain Theorem, especially part b) using theorem 3 of Markov Chain
An auto insurance company classifies each motorist as "high risk" if the motorist has had at least one moving violation during the past calendar year and "low risk" if the motorist has had no violations during the past calendar year. According to the company's data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 90% chance of moving to the high-risk category the next year and a 10% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category? (Round your answers to two decimal places.) high-risk category % low-risk category %
Draw the state diagram for the Markov Model and show the transition probabilities on the diagram.
i) 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.(ii) If volume is low this week then it will be high next week with a probability of 0.2.The manager estimates that the volume is five times as likely to be high as to be low this week.Assume that state 1 is high volume and that state 2 is low volume. Find the transition matrix P for this Markov chain:
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Consider a continuous-time Markov chain with transition rate matrix 0 2 31 Q10 3 2 0/ What are the one-step transition probability matrix of the embedded chain? Enter your answer as a vector of the form ((a₁, b₁, ₁), (a₂, b₂, ₂), (as, bs, cs)) where each of a, b, c, is an integer of the form or a fraction of the form m/n; eg ((1, 1/2, 1/3), (1, 1/2, 1/3), (1, 1/2, 1/3)). Note that there are 8 brackets and 8 commas in total. All should be included. Do not include spaces.
3. Markov Chain Representation Describe a situation from your experience and represent it as a Markov chain. Make sure to explciitly specify both the states and the state-transition probabilities.
PLEASE HELP ME GET THE ANSWER FOR PART B AND IT HAS TO BE FRACTION/INTEGER/ OR EXACT DECIMAL AND THE ASWER I GOT 0.66 FOR FIRST AND 0.99 FOR SECOND AND BOTHER WERE WRONG. The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities. To From Running Down Running 0.90 0.10 Down 0.20 0.80 (a) If the system is initially running, what is the probability of the system being down in the next hour of operation? ANSWER FOR PART A IS 0.10 (b) What are the steady-state probabilities of the system being in the running state and in the down state? (Enter your probabilities as fractions.) Running?1= Your answer must be a fraction, integer, or exact decimal. .66 IS…
2. The day-to-day changes in weather for a certain part of the country form a Markov process. Each day is sunny, cloudy, or rainy. • If it is sunny one day, there is a 70% chance that it will be sunny the following day, a 20% chance it will be cloudy, and a 10% chance of rain. • If it is cloudy one day, there is a 30% chance it will be sunny the following day, a 50% chance it will be cloudy, and a 20% chance of rain. • If it rains one day, there is a 60% chance that it will be sunny the following day, a 20% chance that it will be cloudy and a 20% chance of rain. (a) Create a transition diagram that describes this scenario. (b) Create a stochastic matrix that describes this scenario. Is this scenario ergodic or absorbing? Explain. (c) Suppose that today, there is a 42% chance of sun, 38% chance of clouds, and 20% chance of rain. Using matrix multiplication, predict the weather tomorrow, next Thursday (in 7 days), and in two weeks (in 14 days). (d) Find the eigenvalues and eigenvectors…
Suppose that a basketball player’s success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known:p3,2=0.35, p3, 3=0.25, p3,5=0.4p4,1=0.35, p4,3=0.4, p4,4=0.25p5,1=0.3, p5,2=0.2, p5,4=0.3, p5,5 = 0.2(a) Let T denote the transition matrix. Compute T3. Find the probability that if you start in state #3 you will be in state #5 after 3 steps. (b) Compute the matrix N = (I - Q)-1. Find the expected value for the number of steps prior to hitting an absorbing state if you start in state #3. (Hint: This will be the sum of one of the rows of N.) steps(c) Compute the matrix B = NR. Determine the probability that you eventually wind up in state #1 if you start in state #4.
Please do question 3c with full working out. I'm struggling to understand what to write

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a, 15% of the commuters currently use the public transportation system, wh hs from now 10% of those who are now commuting to work via automobile nsportation will commute via automobile and 80% will continue to use public transition matrix for the Markov chain that describes the change in the mode A