Solutions for College Mathematics for Business, Economics, Life Sciences and Social Sciences, 14th Edition by Barnett (All Chapters included)

College Mathematics for Business,
Economics, Life Sciences and
Social Sciences, 14th Edition by
Raymond A. Barnett




Complete Chapter Solutions Manual
are included




** Immediate Download
** Swift Response
** All Chapters included
** Instructor Answers included

,Table of Contents are given below




1. Linear Equations and Graphs

2. Functions and Graphs

3. Mathematics of Finance

4. Systems of Linear Equations; Matrices

5. Linear Inequalities and Linear Programming

6. Linear Programming: The Simplex Method

7. Logic, Sets, and Counting

8. Probability

9. Limits and the Derivative

10. Additional Derivative Topics

11. Graphing and Optimization

12. Integration

13. Additional Integration Topics

14. Multivariable Calculus

15. Markov Chains

Appendix A: Basic Algebra Review

Appendix B: Special Topics

,The Solutions Manual are organized in reverse order, with the last chapter displayed first, to ensure
that all chapters are included in this document.


15 MARKOV CHAINS


EXERCISE 15-1

6 9 6 9
2. 4 5     24  15 36  35   39 71 4.  3 7   4 5 not defined.
 3 7  

 4  6 9   6 9   4   24  45 69 
6.  5  3 7  not defined. 8.  3 7   5  12  35    47 
         

.7 .3 .7 .3
10. S1  1 0    .7 .3 , S2  .7 .3    .52 .48
.1 .9  .1 .9 

.7 .3 .7 .3
12. S1  .2 .8    .22 .78 , S2  .22 .78    .232 .768
.1 .9  .1 .9 

.7 .3 .7 .3
14. S1  .75 .25    .55 .45 , S2  .55 .45 .1 .9   .43 .57 
 .1 .9   

The transition matrix for Problems 15–20 is
A B
A .5 .5
B .8 .2 

.5 .5 .5 .5
16. S1   0 1    .8 .2 , S2  .8 .2    .56 .44
.8 .2  .8 .2 

.5 .5 .5 .5
18. S1  .9 .1    .53 .47  , S2  .53 .47     .641 .359
.8 .2  .8 .2 

.5 .5 .5 .5
20. S1  .2 .8    .74 .26 , S2  .74 .2 6    .578 .422
.8 .2  .8 .2 

.2 .4 .4  .2 .4 .4 
22. S1   0 0 1 .7 .2 .1  .5 .3 .2 , S2  .5 .3 .2 .7 .2 .1  .41 .32 .27 
.5 .3 .2  .5 .3 .2 

.2 .4 .4  .2 .4 .4 
24. S1  .5 .5 0 .7 .2 .1  .45 .3 .25 , S2  .45 .3 .25 .7 .2 .1  .425 .315 .26
 
.5 .3 .2  .5 .3 .2 

.2 .4 .4  .2 .4 .4 
26. S1  .4 .3 .3 .7 .2 .1  .44 .31 .25 , S2  .44 .31 .25 .7 .2 .1  .43 .313 .257
 

.5 .3 .2  .5 .3 .2 




15-1

, 15-2 CHAPTER 15: MARKOV CHAINS


The transition matrix for problems 27–32 is

.2 .3 .5
P  .1 .8 .1
.4 .2 .4 

.2 .3 .5 .2 .3 .5
28. S1   0 1 0 .1 .8 .1  .1 .8 .1 , S2  .1 .8 .1 .1 .8 .1  .14 .69 .17 
.4 .2 .4  .4 .2 .4 

.2 .3 .5 .2 .3 .5
30. S1  .8 0 .2 .1 .8 .1  .24 .28 .48 , S2  .24 .28 .48 .1 .8 .1  .268 .392 .34
 

.4 .2 .4  .4 .2 .4 

.2 .3 .5 .2 .3 .5
32. S1  .2 .7 .1 .1 .8 .1  .15 .64 .21 , S2  .15 .64 .21 .1 .8 .1  .178 .599 .223
 
.4 .2 .4  .4 .2 .4 

34. The transition matrix for Problems 15–20 is
A B
A .5 .5
P
B .8 .2 

36.




.9 .1
38. .4 .8
 
This matrix cannot be a transition matrix of a Markov chain since the sum of the probabilities in the second
row in not 1 (it is 1.2).

0 1 
40. 1 0 
 
This matrix can be a transition matrix of a Markov chain.

.2 .8
42. .5 .5
 
.9 .1
This matrix cannot be a transition matrix of a Markov chain since it is not a square matrix.