Probability Theory: fall 1997
## Statistics 241/541: Probability Theory (fall 1997)

**Instructor:** David Pollard

** Office:** 24 Hillhouse Avenue

** Office hours:** Wednesday 3:00--5:00

** Email:**
david.pollard@yale.edu

**TA:** Laura McKinney (mckinney@stat.yale.edu)

** Classes:** MWF 9:30-10:20, WLH 207

### Grading

Weekly homework counting for 50% of grade; final exam counting for
other 50%. The midterm test will be marked out of 15. The score will
be 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; it will have little effect on the final grade for the course.)
### WWW site

and other material for the course.
### Computing

Some examples in the text were constructed using MatLab,
a computing environment that is available both on pantheon and at the
StatLab. Familiarity with MatLab (or Mathematica, or some other high
level package) is *not* a requirement of the course, but it
sure would make your life easier.
MatLab m-files
for the calculations and graphics in the notes will be
avilable from the WWW site.

### Description

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