Statistics 241/541: Probability Theory (fall 2005)

Instructor: David Pollard (
Classroom: WLH 208
Time: MWF 9:30-10:20
Office: 24 Hillhouse Avenue
Office hours: Tuesday 3:00 - 5:00
TAs: John Ferguson ( and Stephan Winkler (

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.

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


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.