Please note that the official course website is on Canvas (log in with CNetID), NOT here. This webpage is for those who are interested in STAT 25300/31700 to get an idea of what the course is like.
Click here to view the older STAT 25300/31700 webpage for Winter 2014.
STAT 24400 or 24410 or 25100 or 25150. Or instructor consent.
Introduction to Probability Models (12th or 11th edition) by S. Ross
| Week | Date | Topic and Slides | Textbook Coverage |
|---|---|---|---|
| 1 | M, Jan. 11 | Lecture 1: Definitions of Markov chains, transition probabilities, Ehrenfest diffusion models, discrete queueing models | Sections 4.1 |
| . | W, Jan. 13 | Lecture 2: Chapman-Kolmogorov Equation | Sections 4.2 |
| . | F, Jan. 15 | Lecture 3: Classification of states (recurrent, transient), recurrence and transience of simple random walks | Section 4.3 |
| 2 | M, Jan. 18 | Martin Luther Kings’ Day, No Class | – |
| . | W, Jan. 20 | Lecture 4: Limiting distribution I | Sections 4.4 |
| . | F, Jan. 22 | Lecture 5: Limiting distribution II | Sections 4.4. |
| 3 | M, Jan. 25W, Jan. 27 | Lecture 6: Backward Markov chain, time reversibility, detailed balanced equation, random walk on a weighted graph | Sections 4.8 |
| . | F, Jan. 29 | Lecture 7: Trick of conditioning on the previous step, branching Processes | Sections 4.7. |
| 4 | M, Feb. 1 | Lecture 8: Generating Functions | – |
| . | W, Feb. 3 | Lecture 9: Exponential distributions, memoryless property, definitions of Poisson processes | Section 5.2-5.3 |
| . | F, Feb. 5 | Midterm I, No Class | - |
| 5 | M, Feb. 8 | Lecture 10: Interarrival times of a Poisson process, conditional distribution of interarrival times | Sections 5.3 |
| . | W, Feb. 10 | Lecture 11: Thinning, superposition, “converse” of thinning and superposition, generalization of Poisson processes | Sections 5.3-5.4 |
| . | F, Feb. 12 | Lecture 12: Definitions of continuous-time Markov chains, birth-and-death processes, Chapman-Kolmogorov equation, forward equation, backward equation | Sections 6.2-6.4 |
| 6 | M, Feb. 15 | Lecture 13: Limiting probabilities, time reversibility | Sections 6.5-6.6 |
| . | W, Feb. 17 | Lecture 14: Definition of renewal processes, renewal function, renewal equation | Sections 7.2 |
| . | F, Feb. 19 | Lecture 15: Limit theorems, stopping time, Wald’s equation, elementary renewal theorem. | Section 7.3 |
| . | - | Lecture 16: limit theorems, CLT for renewal processes (Not covered in 2021) | Section 7.3 |
| 7 | M, Feb. 22 | Lecture 17: Renewal Reward Processes, Alternating Renewal Processes | Section 7.4 & 7.5.1 |
| . | W, Feb. 24 | Lecture 18: the inspection paradox; queueing models | Section 7.7 & 8.1 |
| . | F, Feb. 26 | Midterm II, No Class | - |
| 8 | M, Mar. 1 | Lecture 19: Little’s formula, cost identity, birth-death queueing models | Section 8.2.1 & 8.3. |
| . | W, Mar. 3 | Lecture 20: PASTA principle; a Markov chain embedded in M/G/1 | Section 8.2.2, 8.5 |
| . | F, Mar. 5 | Lecture 21: a Markov Chain embedded in G/M/1; G/M/k, M/G/k | Section 8.6, 8.9.3-8.9.4 |
| 9 | M, Mar. 8W, Mar. 10 | Lecture 22&23 Brownian motion as a limit of random walk, conditional distribution; Hitting Time, Maximum, Reflection Principle | Section 10.1-10.2 |
| . | F, Mar. 12 | Lecture 24: Wald’s identities for Brownian motions | - |
| . | - | Lecture 25: The Maximum of Brownian Motion with Drift (not covered in 2021) | Section 10.5 |