Class Meeting: MWF 11:30-12:20 am, Eck117
Name | Office | Telephone | Office Hours | ||
---|---|---|---|---|---|
Instructor | Yibi Huang | Eck104A | 773-834-1024 | yibih@uchicago.edu | Wed 4-5pm in Eck104A or by appointment |
CA | Rishideep Roy | Ryerson N375 | 773-834-3393 | rishideep@galton.uchicago.edu | TuTh 4:30-5:30 in Eck117 or by appointment |
Textbook: Introduction to Probability Models (2010, 10th edition) by S. Ross.[IPM10e]
Complete Syllabus: Click Here
Date | Topics | Homework (Solutions are on Chalk) | |
---|---|---|---|
M | Jan. 07 | Lecture 1: definitions of Markov chains, transition probabilities, Ehrenfest diffusion models, discrete queueing models, Sections 4.1 | HW1Jan7.pdf |
W | Jan. 09 | Lecture 2: Chapman-Kolmogorov Equation. Sections 4.2 | HW2Jan9.pdf |
F | Jan. 11 | Lecture 3: classification of states (recurrent, transient), recurrence and transience of simple random walks. Section 4.3, p.204-210 | HW3: Exercise 4.13, 4.14 on p.277, due Fri, Jan. 18 |
M | Jan. 14 | Lecture 4: Limiting distribution I. Sections 4.4 | No Assignment |
W | Jan. 16 | Lecture 5: Limiting distribution II. Sections 4.4. | HW4Jan16.pdf |
F | Jan. 18 | Lecture 6: backward Markov chain, time reversibility, detailed balanced equation. Sections 4.8 | HW5Jan18.pdf |
M | Jan. 21 | Martin Luther Kings' Day, No Class | |
W | Jan. 23 | Lecture 7: Branching Processes. Sections 4.7. | HW6Jan23.pdf |
F | Jan. 25 | Lecture 8: Generating Functions | HW7Jan25.pdf |
M | Jan. 28 | Lecture 9:
exponential distributions, memoryless property, definitions of Poisson processes. Reading: Section 5.1-5.3 | HW8: Exercise 5.20, 5.22 on p.357 due Mon Feb. 4 |
W | Jan. 30 | Lecture 10: interarrival times of a Poisson process, conditional distribution of interarrival times. Sections 5.3. | HW9Jan30.pdf |
F | Feb. 1 | Lecture 11: thinning, superposition, "converse'' of thinning and superposition, generalization of Poisson processes. Sections 5.3, 5.4 | HW10Feb1.pdf |
M | Feb. 4 | Lecture 12: definitions of continuous-time Markov chains, birth and death processes, Chapman-Kolmogorov equation, forward equation, backward equation. Sections 6.2 - 6.4. | No Assignment |
W | Feb. 6 | Lecture 13: limiting probabilities, time reversibility. Sections 6.5, 6.6. |
Reading: Section 6.1-6.6 (may skip Proposition 6.1 and Example 6.8 on p.382) HW11: Exercise 6.3, 6.5, 6.14, 6.20, 6.23 due Wed Feb. 13. |
F | Feb. 8 | Lecture 14: Definition of renewal processes, renewal function, renewal equation. Sections 7.2. | HW12: Exercise 7.4, 7.5, due Mon Feb 18 (because no class on Fri Feb 15, college break) |
F | Feb. 8 | Midterm Exam, 4-6pm in Eck133. Coverage: Chapter 4-5 | |
M | Feb. 11 | Lectures 15: limit theorems, stopping time, Wald's equation, elementary renewal theorem. Reading: Section 7.3 (Skip Example 7.7) |
HW13: Exercise 7.12, 7.17 (See Exercise 7.11 for the definition of a delayed renewal process), due Mon, Feb. 18 Problems for Self-Study (Do Not Turn In): Exercise 7.8 (See solutions on p.758-759) |
W | Feb. 13 | Lecture 16: limit theorems, CLT for renewal processes. Section 7.3 | No Assignment |
F | Feb. 15 | College Break, No Class | |
M | Feb. 18 | Lecture 17:
Renewal Reward Processes, Alternating Renewal Processes. Reading: Section 7.4 and 7.5.1 |
HW14: Exercise 7.28, 7.32, 7.33, 7.36, due Mon, Feb. 25 Problems for Self-Study (Do Not Turn In): Example 7.13, 7.14, 7.15 on p.442-444, Example 7.25, 7.26 on p.454-457 |
W | Feb. 20 | Lecture 18:
the inspection paradox (Section 7.7), queueing models (Section 8.1) |
HW15: Exercise 7.41, 7.44 on p.492-493, due Wed, Feb. 27 Reading: Section 7.7 Inspection Paradox (p.460-463) Problems for Self Study: Exercise 7.42 (Solutions on p.761) |
F | Feb. 22 | Lecture 19: Little's formula, cost identity (Section 8.2.1), birth-death queueing models (Section 8.3). | HW16Feb22.pdf |
M | Feb. 25 | Lecture 20: PASTA principle (Section 8.2.2) A Markov chain embedded in M/G/1 (Section 8.5) | HW17Feb25.pdf |
W | Feb. 27 | Lecture 21: A Markov Chain embedded in G/M/1 (Section 8.7), G/M/k, M/G/k (Section 8.9.3-8.9.4), Gaussian processes, definition of Brownian motion | HW18Feb27.pdf |
F | Mar. 1 | Lecture 22: Brownian motion as a limit of random walk, conditional distribution (Section 10.1), hitting times, maximum, reflection principle (Section 10.2) | HW19Mar1.pdf |
M | Mar. 4 | Lecture 23: Arcsine law, zero set of Brownian motion | No Assignment |
W | Mar. 6 | Lecture 24: Wald's identities for Brownian motion | HW20Mar6.pdf, due Wed, Mar. 13 |
F | Mar. 8 | Lecture 25: More applications of Wald's identities | HW21Mar8.pdf, due Fri, Mar. 15 |
M | Mar. 11 | Lecture 26: Quadratic Variation. | No Assignment |
W | Mar. 13 | Lecture 27: Ito's Integral, Ito's Formula | No Assignment |
F | Mar. 15 | Reading Period, No Class. | |
M | Mar. 18 | Final Exam, 10:30-1:30pm, Eck133 |