Please do Exercise 3 part A,B,C,D and please show step by step and explain Topic of this questions is Markov Chains 3 [Kelton] There has been much interest in whether industries in the United Statesare moving from the Northeast and North Central regions to the South and West,motivated by the warmer climate, by lower wages, and by less unionization. Hereis the transition matrix for large firms in Electric and Electronic Equipment.NENCSWZNE0.7870000.021NC00.9660.06300.009SW0.11100.03400.937 00.0740.0050.6120.010Z0.102000.3140.954For example, a firm in the Northeast region will be in the West region nextyear with probability 0.111. (The Z entry is a "birth-death" state. For instance,with probability 0.102 a large Electric and Electronic Equipment firm from theNortheast will move out of this system next year: go out of business, move abroad,or move to another category of firm. There is a 0.021 probability that a firm in theNational Census of Manufacturers will move into Electronics, or be created, ormove in from abroad, into the Northeast. Finally, with probability 0.954 a firmout of the categories will stay out, according to this research.)(a) Does the Markov model assumption of lack of history seem justified?Z0.0000(b) Assume that the initial distribution is even, except that the value at Z is 0.9.Compute the vectors for n = 1 through n = 4.(c) Suppose that the initial distribution is this.NENCSW0.00000.6522 0.3478 0.0000Calculate the distributions for n = 1 through n = 4.(d) Find the distribution for n = 50 and n = 51. Has the system settled down toan equilibrium?

note : Since you have posted question with multiple sub parts, we will provide the solution only to…

(a) Does the Markov model assumption of lack of history seem justified? (b) Assume that the initial distribution is even, except that the value at Z is 0.9. Compute the vectors for n = 1 through n = 4. (c) Suppose that the initial distribution is this. NE NC S W 0.0000 0.6522 0.3478 0.0000 for n = 1 through n = 4. Calculate the distributions Z 0.0000

(a) Does the Markov model assumption of lack of history seem justified? (b) Assume that the initial distribution is even, except that the value at Z is 0.9. Compute the vectors for n = 1 through n = 4. (c) Suppose that the initial distribution is this. NE NC S W 0.0000 0.6522 0.3478 0.0000 for n = 1 through n = 4. Calculate the distributions Z 0.0000

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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