A customer always eats lunch either at restaurant A or restaurant B. • The customer never eats at A two days in a row. • If the customer eats at B one day, then the next day she is three times as likely to eat at B as at A. First, we construct the probability transition matrix for the problem. 4= [81] Initially, the customer is equally likely to eat at either restaurant, so x= [ 1 ] Xo
A customer always eats lunch either at restaurant A or restaurant B. • The customer never eats at A two days in a row. • If the customer eats at B one day, then the next day she is three times as likely to eat at B as at A. First, we construct the probability transition matrix for the problem. 4= [81] Initially, the customer is equally likely to eat at either restaurant, so x= [ 1 ] Xo
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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The example is given to solve the problem, please help.
![Example 7.38:
A customer always eats lunch either at restaurant A or restaurant B.
• The customer never eats at A two days in a row.
• If the customer eats at B one day, then the next day she is three times as likely to eat at
B as at A.
First, we construct the probability transition matrix for the problem.
[}
Calculating subsequent state vectors:
A =
Initially, the customer is equally likely to eat at either restaurant, so
[1]
X₁
X₂
X3
-
X₁
X5
Xo
X6
=
=
-
=
=
[
X₁ = [
1 4
0.125
0.875
0.21875
0.78125
0.1953125
0.8046875
0.20117
0.79883
0.19971
0.80029
0.20007
0.79993
0.19998
0.80002
The state vectors appear to converge to the vector
0.2
0.8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7204a7a9-9779-428a-ab98-f09122257236%2F0500a02d-b01e-42c5-993e-105403f605ed%2F7tsei2o_processed.png&w=3840&q=75)
Transcribed Image Text:Example 7.38:
A customer always eats lunch either at restaurant A or restaurant B.
• The customer never eats at A two days in a row.
• If the customer eats at B one day, then the next day she is three times as likely to eat at
B as at A.
First, we construct the probability transition matrix for the problem.
[}
Calculating subsequent state vectors:
A =
Initially, the customer is equally likely to eat at either restaurant, so
[1]
X₁
X₂
X3
-
X₁
X5
Xo
X6
=
=
-
=
=
[
X₁ = [
1 4
0.125
0.875
0.21875
0.78125
0.1953125
0.8046875
0.20117
0.79883
0.19971
0.80029
0.20007
0.79993
0.19998
0.80002
The state vectors appear to converge to the vector
0.2
0.8
Transcribed Image Text:In the first example, what would be the probability transition matrix A if the next day
she is instead 4 times as likely to eat at B as at A?
A
-
8
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