MATH 171


                                HOMEWORK ASSIGNMENTS

Homework should be turned in to the TA by Thursdays in discussion
section.  No late homework will be accepted (but the lowest
homework score will be dropped in computing the final grade).

Graded homework will be returned to the students by the TA.
Questions about the grading of the homework should be directed to
the TA within a week of receiving the homework back.



HW 1) (Due April 9) Section 1.9: #9.1, 9.2, 9.3, 9.4, 9.5, 9.6. 

HW 2) (Due April 16) Section 1.3: #3.1.
                     Section 1.9: #9.7, 9.8, 9.9, 9.17.

HW 3) (Due April 23) Section 1.9: #9.11, 9.12, 9.13, 9.14, 9.16, 9.18, 9.24.

HW 4) (Due April 30) Section 1.5: #5.1, 5.2, 5.3.
                     Section 1.9: #9.22, 9.23, 9.26.

HW 5) (Due May 7)    Section 1.6: #6.1, 6.2, 6.3, 6.4.
                     Section 1.9: #9.39, 9.41.

HW 6) (Due May 14)   Section 1.7: #7.1
                     Section 1.9: #9.46, 9.47, 9.48. 
                     Extra problem: Show that for the general birth and 
                                    death chain defined in Problem 9.46, 
                                    a probability distribution that is 
                                    stationary must satisfy the detailed 
                                    balance condition.

HW 7) (Due May 21)   Section 1.9: #9.35, 9.42, 9.43, 9.50.
                     Extra problem A) In the proof of Theorem 4.5, is the 
                                      coupled chain necessarily aperiodic? 
                                      Prove your answer.
                     Extra problem B) Give an example of a chain with two 
                                      states, which is irreducible but not 
                                      aperiodic, and for which the coupled 
                                      chain in the proof of Theorem 4.5 is 
                                      not irreducible. 

HW 8) (Due May 28)   Section 3.7: # 7.2, 7.3, 7.4, 7.6, 7.17, 7.18, 7.25.
                     Section 4.8: # 8.1, 8.2.

HW 9) (Due June 4)   Section 4.8: # 8.6, 8.7, 8.10, 8.11, 8.16.