## STAT 204: Probability for Applications (Fall 2008)

Instructor: David Aldous (aldous@stat)

Class Time: 1:00pm-2:00pm on MWF in 2 Evans.

Instructor Office hours: T 1:30pm-3:30pm, 351 Evans.

GSI: Partha S. Dey (partha@stat)

Discussion session: M 3:00pm-4:00pm in 340 Evans. Starting September 8.

Office hours: M 4-5pm, W 11-12am, W 4-5pm in 307 Evans.

Textbook: A Second Course in Probability by Sheldon Ross and Erol Pekoz.

Reference: Applied Probability by Kenneth Lange. A longer book, covering most of the same topics in more depth, and covering more topics, is Probability and Random Processes by G. Grimmett and D. Stirzaker

NEW: sample final. Note this year's final is not in the same "write on exam" format -- bring your own paper.

This is a second course in Probability (prerequisite: an undergraduate course) aimed at graduate students in the Statistics, Biostatistics, Computer Science, Electrical Engineering, Business and Economics Departments who expect their thesis work to involve probability. In contrast to STAT 205 (which emphasizes rigorous proof techniques) this course will emphasize describing what's known and how to do calculations in a broader range of probability models. Students are encouraged to learn by doing exercises.

The discussion section is optional and will be used (according to student demand) to expand upon lecture material and to work practice problems.

### Approximate Schedule

The Ross-Pekoz book tends to emphasize proofs while the Lange book emphasizes calculations. I will mostly follow the order of Chapters (below) in Ross-Pekoz while sometimes substituting material from Lange.
1. Chapter 1: Measure Theory and Laws of Large Numbers (plus topics from Lange chapter 2).
2. Chapter 2: Stein's Method and Central Limit Theorems (plus topics from Lange chapter 12).
3. Chapter 3: Conditinal Expectation and Martingales (plus topics from Lange chapter 10).
4. Chapter 4: Bounding Probabilities and Expectation (plus topics from Lange chapter 3).
5. Chapter 5: Markov chains (plus topics from Lange chapter 7).
6. Poisson processes (Lange Chapter 6).
7. Continuous time Markov chains (Lange Chapter 8).
8. Branching processes (Lange Chapter 9).
9. Chapter 7: Brownian Motion (plus topics from Lange chapter 11).

### Homework

Weekly homework posted here by Fridays, due in class each Wednesday (first homework due Wed Sept 10).

50% homework, 50% final.

### Final exam

The campus schedule of classes may give the impression there's no final exam -- but there is. Wednesday, December 17, 5.00 - 8:00 pm, room 334 Evans.

### Handwriting Rule

You can bring to the final exam anything in your own handwriting but nothing else. So you can bring your notes from class, your homework, summaries of the course material you have made - provided these are literally in your own handwriting without electronic intermediation.

### Miscellaneous

Here is a long list of practice final problems compiled several years ago by Shankar Bhamidi. But these are aimed at the Lange book.