STAT 204: Probability for Applications (Fall 2007)

>>>>> I am teaching this course again in Fall 2008. This time the main text will be A Second Course in Probability by Sheldon Ross and Erol Pekoz. But I will also use the Ken Lange book, below. More details later.

Instructor: David Aldous

Class Time: MWF 1:00 - 2:00 in room 289 Cory.

Teaching Assistant: Allan Sly

Discussion session Tuesday 2.00 - 3.00pm, room 334 Evans.

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.

Texts

Required: K. Lange Applied Probability Springer.

This is a short book, corresponding roughly to the lecture material. A longer book, covering most of the same topics in more depth, and covering more topics, is G. Grimmett and D. Stirzaker Probability and Random Processes

The Lange textbook was written for a biostatistics audience but (aside from a few examples) no technical bio knowledge is used.

Approximate Schedule

The basic plan is to cover Chapters 1-11, listed below, taking 1 week for each chapter. This allows time for some slippage and for an overview at the end of the semester.
  1. Basic notions of probability theory [week 1,2]
  2. Calculation of expectations [week 2,3]
  3. Convexity, optimization and inequalities [week 4]
  4. Combinatorics [week 5]
  5. Combinatorial optimization [week 6]
  6. Poisson processes [week 7]
  7. Discrete-time Markov chains [week 8, 9]
  8. Continuous-time Markov chains [week 10]
  9. Branching processes [week 11]
  10. Martingales [week 12, 13]
  11. Diffusion processes [week 13, 14]
and review in week 15.

Homework

Here is a page of Weekly homework exercises which will be updated as the semester progresses. Homework is due in class each Wednesday. As well as the required homework I have listed ``suggested exercises".

Grading

50% homework, 50% final.

Final exam

The campus schedule of classes may give the impression there's no final exam -- but there is. Monday, December 17, 5.00 - 8:00 pm, room 330 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 last year by Shankar Bhamidi.

Office Hours

David Aldous (aldous@stat) Fridays 10.15 - 11.45 in 351 Evans

Allan Sly (sly@stat) Monday 10.00-11.00, Tuesday 9.00-10.00, Friday 3.00-4.00; all in room 307 Evans.

If you email us please put "STAT 204" in subject.