Probability Theory: fall 2005

Statistics 241/541: Probability Theory (fall 2005)

Instructor: David Pollard (david.pollard@yale.edu)
Classroom: WLH 208
Time: MWF 9:30-10:20
Office: 24 Hillhouse Avenue
Office hours: Tuesday 3:00 - 5:00
TAs: John Ferguson (john.ferguson@yale.edu) and Stephan Winkler (stephan.winkler@yale.edu)
Webpage: http://www.stat.yale.edu/~pollard/stat241

A first course in probability theory: probability spaces, random variables, expectations and probabilities, conditional probability, independence, some discrete and continuous distributions, central limit theorem, law of large numbers. After or concurrent with Mathematics 120a or b or equivalents.

syllabus
(with table showing
material covered in each lecture) notes (no prescribed text);
lecture notes from 1997 and 2000 supplementary references &
miscellaneous course materials midterm test;
final exam

homework
(including solutions) computing email correspondence
(homework, office hours, etc.) ~~FAQ~~;
~~Life after 241/541~~

Grading

weekly homework counting for 50% of grade;
no late homeworks without Dean's note;
no sheet accepted after solutions posted on web;
boxplots of scores on problem sets and midterm test posted on web.
I have not yet decided how much cooperation to allow on homeworks. At the very least I will expect groups to declare their intention to cooperate. Modified homework policy, as of 2 October 2005.
final exam counting for other 50%
midterm test marked out of 15, with score added to the total points scored on the problem sets
(In other words, the midterm will give students some idea about where they stand in the course, but it will have little effect on the final grade for the course.)

Text and references Detailed notes will be available for free to Yale students from the WWW site. The notes will be in Adobe Acrobat pdf format. There is no prescribed text, but you might find some of the supplementary references helpful.

What I intend to cover

Probability theory gives a systematic method for describing randomness and uncertainty. This course will explain the rules for manipulating random variables, probabilities, and expectations, with emphasis on the role of conditioning. The theory will be presented and motivated through a sequence of applications, ranging from the (traditional, boring) calculation of probabilities for card games to (more involved, more interesting) stochastic models.

The coin tossing model will generate the standard discrete distributions: Binomial, Poisson, geometric, negative binomial. The Poisson process, the continuous time analog of coin tossing, will generate the standard continuous distributions: exponential and gamma.

Normal approximations and calculations related to the multivariate normal distribution will exercise the multivariable calculus skills of the class (or provide a crash course in multiple integrals).

Applications to include topics like: Markov chains; the probability theory of games, gambling, and insurance; coding theory; queueing theory; branching processes; geometric probability and stereology; (maybe) analysis of algorithms.

syllabus (with table showing material covered in each lecture)	notes (no prescribed text); lecture notes from 1997 and 2000	supplementary references & miscellaneous course materials	midterm test; final exam
homework (including solutions)	computing	email correspondence (homework, office hours, etc.)	~~FAQ~~; ~~Life after 241/541~~