Statistics 241/541: Probability Theory (fall 2005)
Instructor: David Pollard
(david.pollard@yale.edu)
Classroom: WLH 208
Time: MWF 9:3010:20
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.
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.