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

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.