C: ANSWERS TO SELECTED PROBLEMS

Chapter 9.1, Transition Matrices

1. 3. 44.4%.

5. 42.9% Taylor’s; 57.1% Sower’s. 7. Is a transition matrix.

9. Not a transition matrix, the sum of the elements in last row is not 1.

11. [a] [0.48 0.52], [b] [0.392 0.608]. 13. ; 55%.

15. , Approximately 40%. 17. 64%.

19. 25%. 21. 49.6%.

23. ; .

25. ; ; 20%. 27. 8.5%.

29. No.

Chapter 9.2, Regular Markov Chains

1. Yes. 3. No.

5. No. 7. No.

9. Yes. 11. .

13. [a] Yes, [b] No, [c] No. 15. .

17. [a] Yes , [b] No, [c] No.

19. [a] Yes , [b] No, [c] Yes .

21. 44%. 23. .

25. 58%. 27. .

Chapter 9.3, Absorbing Markov Chains

1. State 4. 3. Yes.

5. No. 7. , 40%, 60%, 0%.

9. [a] 0, [b] approximately 18. 11. [a] States 1 and 2; Yes, [b] None; No.

13. [a] State 3;Yes, [b] States 2 and 4;Yes. 15. 47%.

17. 6%; 99%. 19. 67%.

21. 4 times. 23. 60%.

Chapter 9.4, Chapter Review

1. None. 3. None.

5. Irreducible. 7. .

9. . 11. [a] , [b] ~78%, [c] ~75%.

13. [a] , [b] ~30%, [c] 0. 15. 2.