Math/Stats 525: Probability Theory — Fall 2014


Instructor: Michael Zieve   
Office Hours: Tuesday 11:40–1:00 and Friday 3:30–4:30 in 3835 East Hall
Class: Tuesday and Thursday, 1:10–2:30 in 4044 Randall Harrison Lab

For the course logistics including details about grading and expected work, see the syllabus.

Lecture Schedule and Homework:
  1. Sep. 2, Tu.  Sections 1.2–1.5.  Homework: 5–10, 15, 48 of chapter 1
  2. Sep. 4, Th.  Sections 1.6–2.2.  Homework: 17 (first question), 20, 30, 39 of chapter 1, and 2, 3, 8, 9 of chapter 2
  3. Sep. 9, Tu.  Sections 2.3–2.4.1.  Homework: 14, 16, 30, 32, 33 of chapter 2
  4. Sep. 11, Th.  Sections 2.4.2–2.5.3.  Homework: 40, 49, 53, 56, 58 of chapter 2
  5. Sep. 16, Tu.  Section 2.5.3.  Homework: 42, 51, 55, 59 of chapter 2
  6. Sep. 18, Th.  Sections 2.5.4–2.6.  Homework: 60, 62, 74 of chapter 2
  7. Sep. 23, Tu.  Section 2.6  Homework: 61, 63 of chapter 2
  8. Sep. 25, Th.  Section 2.6  Homework: 71, 76, 77, 78 of chapter 2
  9. Sep. 30, Tu.  Section 2.8  Homework: 67, 68(a) of chapter 2
  10. Oct. 2, Th.  Section 2.8  Homework: 68(b), 69, 80 of chapter 2
  11. Oct. 7, Tu.  Sections 3.1–3.2.  Homework: prepare for the midterm
  12. Oct. 9, Th.  Section 3.3.  Homework: prepare for the midterm
  13. Oct. 14, Tu.  No class: Fall Study Break
  14. Oct. 16, Th.  Midterm, covering chapters 1 and 2
  15. Oct. 21, Tu.  Sections 3.4–3.5.  Homework: 3, 4, 7, 11, 15, 26, 27 of chapter 3
  16. Oct. 23, Th.  Sections 4.1–4.2.  Homework: 1, 3, 4 of chapter 4
  17. Oct. 28, Tu.  Section 4.3.  Homework: 5, 6, 8, 14, 16 of chapter 4
  18. Oct. 30, Th.  Section 4.3.  Homework: 12, 15, 18 of chapter 4
  19. Nov. 4, Tu.  Section 4.4.  Homework: 24, 31, 33, 35, 36 of chapter 4
  20. Nov. 6, Th.  Sections 4.4–4.5.1.  Homework: 41, 45, 46, 57, 61 of chapter 4
  21. Nov. 11, Tu.  Section 4.8.  Homework: 38, 47, 68 of chapter 4
  22. Nov. 13, Th.  Section 4.8.  Homework: 70, 72, 73, 74 of chapter 4
  23. Nov. 18, Tu.  Section 4.9.  Homework: Describe (with proof) exactly when the Markov chain defined on pp. 261–262 is irreducible, and when it has period 1 (i.e., is aperiodic). Note that if these conditions hold then, since the Markov chain has a stationary distribution (because it is reversible), the Markov chain converges to its stationary distribution for any choice of probability distribution on X0.
  24. Nov. 20, Th.  Section 5.2.2.  Homework: 1, 2, 3, 4, 5 of chapter 5
  25. Nov. 25, Tu.  Section 5.2.3.  Suggested practice problems (not to be handed in): 9, 25, 30 of chapter 5
  26. Dec. 1, Tu.  Sections 5.3.1–5.3.4.  Suggested practive problems (not to be handed in): 37 and 43 of chapter 5
    27. There will be no more quizzes, and the practice problems listed above do not need to be handed in (but they will be tested on the midterm).
  27. Dec. 3, Th.  Review for midterm.
  28. Dec. 9, Tu.   Midterm in CC Little Room 2548 at the usual class time.