Class Meeting: MWF 11:30-12:20 am, Eck117
Name | Office | Office Hours | ||
---|---|---|---|---|
Instructor | Yibi Huang | Eckhart 7 | yibih@uchicago.edu | Mon 5-6pm in Eck 131 or by appointment |
CA | Wei Su | Eckhart 8 | weisu@galton.uchicago.edu | Tue 4-5pm in Eck131 Thur 2-3pm in Eck131 or by appointment |
Textbook: Introduction to Probability Models (2010, 10th edition) by S. Ross.[IPM10e]
Complete Syllabus: Click Here
Date | Topics and Slides | Assignments (Solutions are posted on Chalk) | |
---|---|---|---|
M | Jan. 06 | Severe weather, class canceled | |
W | Jan. 08 | Lecture 1: Definitions of Markov chains, transition probabilities, Ehrenfest diffusion models, discrete queueing models, Sections 4.1 | HW1Jan8.pdf |
F | Jan. 10 | Lecture 2: Chapman-Kolmogorov Equation. Sections 4.2 | HW2Jan10.pdf |
M | Jan. 13 | Lecture 3: Classification of states (recurrent, transient), recurrence and transience of simple random walks. Section 4.3, p.204-210 | HW3.txt |
W | Jan. 15 | Lecture 4: Limiting distribution I. Sections 4.4 | No Assignment |
F | Jan. 17 | Lecture 5: Limiting distribution II. Sections 4.4. | HW4Jan17.pdf |
M | Jan. 20 | Martin Luther Kings' Day, No Class | |
W | Jan. 22 | Lecture 6: Backward Markov chain, time reversibility, detailed balanced equation. Sections 4.8 | HW5Jan22.pdf |
F | Jan. 24 | Lecture 7: Trick of one-step conditioning, branching Processes. Sections 4.7. | HW6.txt |
M | Jan. 27 | Lecture 8: Generating Functions | HW7Jan27.pdf |
W | Jan. 29 | Lecture 9:
Exponential distributions, memoryless property, definitions of Poisson processes. Reading: Section 5.1-5.2 | HW8: Exercise 5.20, 5.22, 5.22 on p.357 due Fri Feb. 7 |
F | Jan. 31 | Lecture 10: Interarrival times of a Poisson process, conditional distribution of interarrival times. Sections 5.3. | HW9.txt |
M | Feb. 3 | Lecture 11: Thinning, superposition, "converse'' of thinning and superposition, generalization of Poisson processes. Sections 5.3, 5.4 | HW10.txt |
W | Feb. 5 | 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 |
F | Feb. 7 | Lecture 13: Limiting probabilities, time reversibility. Sections 6.5, 6.6. | HW11.txt |
M | Feb. 10 | Lecture 14: Definition of renewal processes, renewal function, renewal equation. Sections 7.2. | HW12.txt |
M | Feb. 10 | Midterm Exam, 6:30-8:30pm in Eck133. Read the Midterm Exam Coverage and Study Guide Here is a Sample Midterm Exam and its solutions for practice (2014/02/12) Solutions to the Midterm Exam | |
W | Feb. 12 | Lectures 15: Limit theorems, stopping time, Wald's equation, elementary renewal theorem. Reading: Section 7.3 (Skip Example 7.7) | HW13.txt |
F | Feb. 14 | College Break, No Class | |
M | Feb. 17 | Lecture 16: limit theorems, CLT for renewal processes. Section 7.3 | HW14.txt |
W | Feb. 19 | Lecture 17:
Renewal Reward Processes, Alternating Renewal Processes. Reading: Section 7.4 and 7.5.1 |
HW15.txt |
F | Feb. 21 | Lecture 18:
the inspection paradox (Section 7.7), queueing models (Section 8.1) | HW16.txt |
M | Feb. 24 | Lecture 19: Little's formula, cost identity (Section 8.2.1), birth-death queueing models (Section 8.3). | HW17Feb24.pdf |
W | Feb. 26 | Lecture 20: PASTA principle (Section 8.2.2) A Markov chain embedded in M/G/1 (Section 8.5) | HW18Feb26.pdf |
F | Feb. 28 | 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 | HW19Feb28.pdf |
M | Mar. 3 | Lecture 22: Brownian motion as a limit of random walk, conditional distribution. Section 10.1 | No Assignment |
W | Mar. 5 | Lecture 23: Hitting Time, Maximum, Re?ection Principle. Section 10.2 | HW20Mar5.pdf |
F | Mar. 7 | Lecture 24: Wald's identities for Brownian motion | No Assignment |
M | Mar. 10 | Lecture 25: More applications of Wald's identities | HW21Mar10.pdf, due Fri, Mar. 15 |
W | Mar. 12 | Lecture 26: Quadratic Variation. | No Assignment |
F | Mar. 14 | Reading Period, No Class. | |
W | Mar. 19 | Final Exam, 4-6pm, in Eck133 Read the Final Exam Coverage and Study Guide (2014/03/21) Solutions to the Final Exam |