(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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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 States
are 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. Here
is the transition matrix for large firms in Electric and Electronic Equipment.
NE
NC
S
W
Z
NE
0.787
0
0
0
0.021
NC
0
0.966
0.063
0
0.009
S
W
0.111
0
0.034
0
0.937 0
0.074
0.005
0.612
0.010
Z
0.102
0
0
0.314
0.954
For example, a firm in the Northeast region will be in the West region next
year 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 the
Northeast 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 the
National Census of Manufacturers will move into Electronics, or be created, or
move in from abroad, into the Northeast. Finally, with probability 0.954 a firm
out of the categories will stay out, according to this research.)
(a) Does the Markov model assumption of lack of history seem justified?
Z
0.0000
(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.
NE
NC
S
W
0.0000
0.6522 0.3478 0.0000
Calculate the distributions for n = 1 through n = 4.
(d) Find the distribution for n = 50 and n = 51. Has the system settled down to
an equilibrium?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2F44348144-65d5-47de-8e1a-831d764f10bf%2Fm2n7b15_processed.png&w=3840&q=75)
Transcribed Image Text:3 [Kelton] There has been much interest in whether industries in the United States
are 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. Here
is the transition matrix for large firms in Electric and Electronic Equipment.
NE
NC
S
W
Z
NE
0.787
0
0
0
0.021
NC
0
0.966
0.063
0
0.009
S
W
0.111
0
0.034
0
0.937 0
0.074
0.005
0.612
0.010
Z
0.102
0
0
0.314
0.954
For example, a firm in the Northeast region will be in the West region next
year 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 the
Northeast 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 the
National Census of Manufacturers will move into Electronics, or be created, or
move in from abroad, into the Northeast. Finally, with probability 0.954 a firm
out of the categories will stay out, according to this research.)
(a) Does the Markov model assumption of lack of history seem justified?
Z
0.0000
(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.
NE
NC
S
W
0.0000
0.6522 0.3478 0.0000
Calculate the distributions for n = 1 through n = 4.
(d) Find the distribution for n = 50 and n = 51. Has the system settled down to
an equilibrium?
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