(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, nextThursday (in 7 days), and in two weeks (in 14 days).(d) Find the eigenvalues and eigenvectors for this transition matrix.(e) In the long run, what percentage of days will be sunny? Cloudy? Rainy? Explain. The day-to-day changes in weather for a certain part of the country form a Markovprocess. Each day is sunny, cloudy, or rainy.• If it is sunny one day, there is a 70% chance that it will be sunny the followingday, 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, a50% 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.

We are given here that P(S->S) = 0,4, P(S->C)=03, P(S-R)=0.3 Also, we are given that:…

Answered: The day-to-day changes in weather for a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Central topic markov chains: Every summer the Yates de los Lagos owners association decides if its annual regatta will be held in June, July or August. If it takes place in June, the probability of good weather is ¾; and if these conditions exist, the regatta of the next year it will be done in June with probability 2/3, in July with probability 1/6 or in August with probability 1/6; but if there is bad weather, next year's regatta will take place in July or August with equal probabilities. If the competition is held in July, good and bad weather have equal probabilities; if there is good weather, the next year's regatta will be held in July; If there is bad weather, the next regatta will take place in August with probability of 2/3 or in June with probability of 1/3. If the regatta takes place in August, the probability of good weather is 2/5; and if there are good conditions atmospheric conditions, next year's regatta will take place in July or August, with equal probabilities; but…
3. Consider an undiscounted Markov decision process with three states 1, 2, 3, with respec- tive rewards -1, -2,0 for each visit to that state. In states 1 and 2, there are two possible actions: a and b. The transitions are as follows: • In state 1, action a moves the agent to state 2 with probability 0.8 and makes the agent stay put with probability 0.2. In state 2, action a moves the agent to state 1 with probability 0.8 and makes the agent stay put with probability 0.2. . In either state 1 or state 2, action b moves the agent to state 3 with probability 0.1 and makes the agent stay put with probability 0.9. Find the optimal policy that minimises the expected total cost and find the corresponding value function.
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…
TOPIC: MARKOV CHAINSA market research firm conducted a household survey regarding preferences for three brands of detergents.three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months.consecutive months. The results of the survey are as follows: Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand.for the "Clean" brand. C) If the pattern of profit and loss does not change in the following months, how many housewives are estimated to prefer each brand at the end of month 2?
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).
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
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
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
In a hotel, each employee is in one of three possible job classifications, and changes that classifications (independently) according to a Markov chain with transition probabilities. What percentage of employees are in each classification?

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