Math 331: An introduction to probability and Markov chain models

• Meeting time and place: Tuesdays and Thursdays, 11:00 AM - 12:15 PM, Van Vleck B119.
• Office Hours: Mondays 9:00 AM - 10:30 AM, Wednesday 10:30 AM - 12:00 PM.
• Syllabus
• Final exam: 2:45 PM - 4:45 PM, Thursday, December 18 (room is still to be decided).

Exams:

Exam 1 set for Thursday, October 2nd. Will cover Chs 1 - 3 and sections 4.1, 4.2, and 4.3. Short review notes. Here is an Answer Key.

Exam 2 is set for Thursday, November 6th from 7:30 - 8:45 PM. Will cover all material from last exam up through section 8.3. Here is an Answer Key.

Exam 3 is set for Thursday December 4th in class. It will cover sections 9.1, 10.1, 10.2, 10.3, and 11.1 - 11.5. Here is an Answer Key.

The Final Exam time and place are set: 2:45 PM on Thursday, December 18th in room B119, which is simply our normal classroom. The exam is cumulative.

Homework and reading assignments:

Week 1 (HW Due Tuesday of Week 2):

1. Section 1.2. Lecture Notes. HW: pgs.   9 - 11, #'s 1, 2, 3, 9, 10, 20. Solutions.
2. Section 1.3. Lecture Notes.
3. Section 1.4. Lecture Notes. HW: pgs.   23 - 26, #'s 5, 10, 13, 17, 25. Solutions.

Week 2 (HW Due Tuesday of Week 3):

1. Sections 1.5, 1.6. Lecture Notes. HW: pg.   34 #'s 1, 3, 4, 5, 10. Solutions.
2. Section 2.2. Lecture Notes. HW: pgs.   44, 45 #'s 1, 3, 5, 14, 15, 17. Solutions.
3. Section 2.3. Lecture Notes. HW: pgs.   50 - 53 #'s 1, 6, 10, 13, 15. Solutions.
4. Section 2.4. Lecture Notes. HW: pgs.   63 - 66 #'s 1, 2, 7, 13, 19, 30. Solutions.

Week 3:

1. Section 3.1. Lecture Notes. HW: pgs.   82 - 84 #'s 2, 3, 8, 9, 18. Solutions.
2. Section 3.2. Lecture Notes with Section 3.1. HW: pgs.   87 - 88 #'s 1, 6, 10. Solutions.
3. Section 3.3. Lecture Notes. HW: pgs.   96 - 97 #'s 1, 7, 9, 13. Solutions.
4. Section 3.4. Lecture Notes with Section 3.3. HW: pgs.   105 - 106 #'s 1, 2, 8. Solutions.

Week 4:

1. Section 3.5. Lecture Notes. HW: pgs.   119 #'s 2, 4, 15, 17, 29. Solutions.
2. Section 4.1. Lecture Notes.
3. Section 4.2. Lecture Notes. HW: pgs.   150 - 152. #'s 1, 4, 5, 6, 7, 16. Solutions.
4. Section 4.3. Lecture Notes. HW: pgs.   157 - 158. #'s 1, 3, 4, 7, 8, 10. (WILL NOT BE COLLECTED) Solutions.

Week 5:

1. Section 4.4. Lecture Notes. HW: pgs.   173 - 174. #'s 2, 3, 7, 11, 12. Solutions.
2. Test 1.

Week 6:

1. Section 4.5. Lecture Notes. HW: pg.   182. #'s 3, 4, 5, 7, 8. Solutions.
2. Section 4.6. Lecture Notes. HW: pg.   185. # 2. Solution.
3. Extra assignment on casino problem is here. Solution.

Week 7:

1. Section 5.1. Lecture Notes. HW: pgs.   196 - 197. #'s 1, 3, 4, 8, 13, 20. For number four, assume they mean "exactly two 9's". Solutions.
2. Section 5.2. Lecture Notes. HW: pgs.   211 - 212. #'s 3, 7, 11, 15. Solutions.

Week 8:

1. Section 5.3. Lecture Notes. HW: pgs.   224 - 226. #'s 3, 5, 9, 15, 16. Solutions.

Week 9:

1. Chapter 6. Lecture Notes. HW: pgs.   238 - 239. #'s 2, 3, 4. Also, 254 - 255. #'s 1, 2, 4. 6.1 Solutions. 6.3 Solutions.
2. Chapter 7. Lecture Notes.
3. Section 8.1. Lecture Notes. HW: pgs.   325 - 326. #'s 1, 2, 3, 4, 5, 7. Solutions.

Week 10:

1. Section 8.2. Lecture Notes. HW: pgs.   339 - 340. #'s 1, 2, 3, 5, 7, 8. Solutions.
2. Section 8.3. Lecture Notes. HW: pgs.   353 - 355. #'s 1, 3, 5 (just discrete case), 13. Solutions.
3. Section 9.1. Lecture Notes. HW: pgs.   383 - 3384. #'s 1, 3, 5. Solutions.
4. Section 10.1. Lecture Notes and examples. HW: pgs.   383 - 384. #'s 3, 5, 11, 13. Solutions.

Week 11:

1. Section 10.2. Lecture Notes. HW: pgs.   424 - 425. #'s 4, 5, 7, 9. Solutions.
2. Section 10.3. Lecture Notes. HW: pgs.   433 - 434. #'s 1, 5, 6. Solutions.

Week 12:

1. Section 11.1. Lecture Notes. HW: pgs.   465 - 466, #'s 1, 3, 6, 7, 9, 17. Solutions.
2. Section 11.2. Lecture Notes. HW: pgs.   474, #'s 2, 6, 8. Solutions.
3. Section 11.3. Lecture Notes. HW: pgs.   484 - 485, #'s 1, 2, 3, 4, 5, 11, 16 (k > 0). Solutions.
4. Section 11.4. Lecture Notes. HW: pg.   497, #'s 2, 4. Solutions.

Week 13:

1. Section 11.5. Lecture Notes. HW: pg.   497, #'s 2, 6, 8. Solutions.

Week 14:

1. First Markov chain notes. Lecture Notes. The homework is on the notes.
2. Test 3.

Week 15:

1. First Markov chain notes. Lecture Notes. The homework is on the notes. Solutions.
2. Second Markov chain notes. Lecture Notes. The homework is on the notes. Solutions.
3. Third Markov chain notes. Lecture Notes.