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:
- Sep. 2, Tu. Sections 1.2–1.5. Homework: 5–10, 15, 48 of chapter 1
- 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
- Sep. 9, Tu. Sections 2.3–2.4.1. Homework: 14, 16, 30, 32, 33 of chapter 2
- Sep. 11, Th. Sections 2.4.2–2.5.3. Homework: 40, 49, 53, 56, 58 of chapter 2
- Sep. 16, Tu. Section 2.5.3. Homework: 42, 51, 55, 59 of chapter 2
- Sep. 18, Th. Sections 2.5.4–2.6. Homework: 60, 62, 74 of chapter 2
- Sep. 23, Tu. Section 2.6 Homework: 61, 63 of chapter 2
- Sep. 25, Th. Section 2.6 Homework: 71, 76, 77, 78 of chapter 2
- Sep. 30, Tu. Section 2.8 Homework: 67, 68(a) of chapter 2
- Oct. 2, Th. Section 2.8 Homework: 68(b), 69, 80 of chapter 2
- Oct. 7, Tu. Sections 3.1–3.2. Homework: prepare for the midterm
- Oct. 9, Th. Section 3.3. Homework: prepare for the midterm
- Oct. 14, Tu. No class: Fall Study Break
- Oct. 16, Th. Midterm, covering chapters 1 and 2
- Oct. 21, Tu. Sections 3.4–3.5. Homework: 3, 4, 7, 11, 15, 26, 27 of chapter 3
- Oct. 23, Th. Sections 4.1–4.2. Homework: 1, 3, 4 of chapter 4
- Oct. 28, Tu. Section 4.3. Homework: 5, 6, 8, 14, 16 of chapter 4
- Oct. 30, Th. Section 4.3. Homework: 12, 15, 18 of chapter 4
- Nov. 4, Tu. Section 4.4. Homework: 24, 31, 33, 35, 36 of chapter 4
- Nov. 6, Th. Sections 4.4–4.5.1. Homework: 41, 45, 46, 57, 61 of chapter 4
- Nov. 11, Tu. Section 4.8. Homework: 38, 47, 68 of chapter 4
- Nov. 13, Th. Section 4.8. Homework: 70, 72, 73, 74 of chapter 4
- 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.
- Nov. 20, Th. Section 5.2.2. Homework: 1, 2, 3, 4, 5 of chapter 5
- Nov. 25, Tu. Section 5.2.3. Suggested practice problems (not to be handed in): 9, 25, 30 of chapter 5
- Dec. 1, Tu. Sections 5.3.1–5.3.4. Suggested practive problems (not to be handed in): 37 and 43 of chapter 5
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).
- Dec. 3, Th. Review for midterm.
- Dec. 9, Tu. Midterm in CC Little Room 2548 at the usual class time.