3. Draw a transition diagram corresponding to the following stochastic matrix: ГО.2 0.6 0.17 A = 0.1 0.2 0.9] Lo.7 0.2
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Draw a transition diagram corresponding to the following stochastic matrix. refer to the image, please
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- Let's consider a supermarket with three cash registers. The operation of the cash registers is checked daily, and if a register is found to be faulty, it is sent to the workshop for repairs. The probability of a working cash register breaking down is 1/5, and the probability of a cash register undergoing repair becoming operational is 3/5. The processes of breakdown and repair of cash registers are independent of each other. 1. (25 pts) Model this problem using a discrete time Markov chain. Present the transition probability matrix. 2. (15 pts) What is the long-run proportion of days when none of the cash registers are operational?Q17. Suppose M is a stochastic matrix representing the probabilities of transitions each month. Compute the matrix of compounded transition probabilities for 3 months into the future, or M³. (Note, prior to multiplying matrices, the given components of M must be used to fill in the missing components [**] such that M is a stochastic matrix.) M = 0.55 ** ** 0.90 What is m22 in the matrix M³? (Round to 3 decimal places.)A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of rainy and drought for known initial year.(a) Write out the stochastic matrix.(b) Find the probabilities for:(i) Year 1(ii)
- If possible, fill in the missing values to make A a doubly stochastic matrix. (If not possible, enter IMPOSSIBLE.) - [ 0.3 a = b = A = a 0.3 X XLet 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.…Discuss two extensions to the original GARCH (p,q) model and explain additional characteristics of financial data they might be able to capture.
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- ↑ The 1990 census reported that 32% of the households in Middletown were homeowners and the remainder were renters. During the next decade, 10% of the homeowners became rent and the rest continued to be homeowners. Similarly, 14% of the renters became homeowners and the rest continued to rent (A) Fill in the appropriate transition matrix for this process. Homeowners Homeowners Renters Renters AR NEI've created a Correlation Matrix in Microsoft Excel. I need to identify 4 pairs of variables that have the highest correlation. How would I do this? The matrix is attached to this question.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