Q18. Suppose M is a stochastic matrix representing the probabilities of transitionseach day. Compute the matrix of compounded transition probabilities for 2 days intothe future, or M². (Note, prior to multiplying matrices, the given components of Mmust be used to fill in the missing component [**] such that M is a stochastic matrix.)M =What is0.800.140.06m320.070.62**0.350.410.24in the matrix M²? (Round to 3 decimal places.)

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Answered: Q18. Suppose M is a stochastic matrix…

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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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
7.7q4
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.

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