Suppose it is known that in the city of Golden the weather is either "good" or "bad". If theweather is good on any given day, there is a 2/3 chance it will be good the next day. If theweather is bad on any given day, there is a 1/2 chance it will be bad the next day.a) Find the stochastic matrix P for this Markov chain.b) Given that on Saturday there is a 100% chance of good weather in Golden, use thestochastic matrix from part (a) to find the probability that the weather on Monday will be good.The initial state xo =c) Over the long run, what is the probability that the weather in Golden is good?

Answered: Image /qna-images/answer/f1085b88-478a-4460-a610-4626a960013a.jpg

Answered: Suppose it is known that in the city of…

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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Let us consider the population of people living in a city and its suburb and the migration within this population from the city and the suburbs to the city and the suburbs. The migration of these populations from and to each other is given by a stochastic matrix [.95 .03] P = |.05 .97 The entries in this matrix were obtained from collected data that demonstrates individuals are 95 % likely to remain in the city, 5 % likely to move from the city to the suburbs, 3 % likely to move from the suburbs to the city, and 97 % likely to remain in the suburbs. Now suppose in the year 2000 60 % or .6 percent of people live in the city and 40 % or .4 percent of people live in the suburbs. What will be the percentage of people living in the city be in the year 2001? What will be the percentage of people living in the suburbs be in 2002? Hint: Recall, for a general Markov Chain (S, ro, P) the initial vector ro is required to merely be a probability vector, that is, a vector whose entries add up to 1.…
Show full answers and steps to part d) and e) using Markov Chain Theory. Please explain how you get to the answers without using excel, R or stata
A businessman is shipping a machine to another country. The cost of overhauling is $2700. If the machine fails in operation in the other country, it will cost $5500 in lost production and repairs. He estimates the probability that it will fail at 0.3 if it is not overhauled, and 0.2 if it is overhauled. Neglect the possibility that the machine might fail more than once in the 4 years (a) Prepare a payoff matrix. (b) What should the businessman do to minimize his expected costs? (a) Fill in the entries of the payoff matrix Fails Does Not Fail 8 81 (b) Would overhauling the machine before shipping minimize the businessman's expected costs? Overhaul Does Not Overhaul CETT OYes O No
(8) Every year, each employee at a large company must select one of two healthcare plans. It is expected that 15% of the employees currently using plan A will switch to plan B and that 25% of the employees currently using plan B will switch to plan A. Out of the company's 1000 employees, 450 are currently enrolled in plan A. (a) Use a stochastic matrix to predict how many employees will be enrolled in each plan next year. (b) Use a stochastic matrix to predict how many employees will be enrolled in each plan in five years.
Anne and Barry take turns rolling a pair of dice, with Anne going first. Anne’s goal is to obtain a sum of 3, while Barry’s goal is to obtain a sum of 4. The game ends when either player reaches his goal,and the one reaching the goal is the winner. Define a Markov Chain to model the problem.
A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impossible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.
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).
Please help to solve
Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct
The main topic is Markov Chains:Students in Geology class never know what is going to happen in the class, as the teacher may: give them a pop quiz, take them to field practice, analyze the topic of the day, or lecture on a special topic.If one day there is a test, the next day there is always a field practice.If one day there is field practice, the next day there is no practice or test, but there is still a chance of the day's topic or special lecture.of the day or of the special lecture.If on a certain day the topic is tested, the probabilities for the next day are ¼ for the test, 1/6 for the topic and 1/3 for the lecture.and 1/3 for the lecture.If one day there is a lecture, the odds for the next day are ¼ for the test, 1/8 for the practice, 1/8 for the topic analysis and ½ for the lecture.for the analysis of the topic and ½ for the lecture.One of the students has calculated that they can expect quizzes 43/287 of the lecture days; field practice72/287 of the class days; topic…
Answer the following questions.
A square matrix is said to be doubly stochastic if itsentries are all nonnegative and the entries in each row andeach column sum to 1. For any ergodic, doubly stochasticmatrix, show that all states have the same steady-stateprobability.

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