**Question 18**: Suppose \( M \) is a stochastic matrix representing the probabilities of transitions each day. Compute the matrix of compounded transition probabilities for 2 days into the future, or \( M^2 \). (Note, prior to multiplying matrices, the given components of \( M \) must be used to fill in the missing component \([**]\) such that \( M \) is a stochastic matrix.)\[M = \begin{bmatrix}0.80 & 0.07 & 0.35 \\0.14 & 0.70 & 0.41 \\0.06 & ** & 0.24\end{bmatrix}\]What is \( m_{32} \) in the matrix \( M^2 \)? (Round to 3 decimal places.)

from given M=0.800.070.350.140.700.410.06∗0.24

Answered: Q18. Suppose M is a stochastic matrix…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

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Q2. Consider a company that is going to build a new manufacturing system and would like to determine the long-run (steady-state) mean hourly throughput of their system after it has been running long enough for workers to know their jobs and for mechanical difficulties to have been worked out. The system will operate continuously 24 hours a day for 7 days a week. Let N; be the number of parts manufactured in the ih hour. If the stochastic process N1, N2, .. has a steady-state distribution with corresponding random variable N, then we are interested in estimating the steady-state mean v = E(N).
3. Construct a model of population flows between cities, suburbs, and nonmetropolitan areas of the United States. Their respective populations in 2022 were 80 million, 175 million, and 52 million. The stochastic matrix giving the probabilities of the moves is (from) (to) city suburb nonmetro 0.96 0.01 0.015 city 0.03 0.98 0.005 suburb 0.01 0.01 0.98 nonmetro Predict the populations of city, suburban, and nonmetropolitan areas for 2023, 2024, and 2025. If a person was living in the city in 2022, what is the probability the person will be living in a nonmetropolian area in 2024?
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.)
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 X
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.…
what is the solution?
60. The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P= .4 .2 .25 .2 .3 .2 .1 .2 .2 .4 25 50 .1 .4 .3 If Xo = 1 (a) find the probability that state 3 is entered before state 4; (b) find the mean number of transitions until either state 3 or state 4 is entered.
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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