## Applied Probability

STAT 331, Fall 2005

Rice University

This course covers the basic concepts of Probability Theory and Statistics.
Targeted at undergraduate students it balances motivation, rigor and application of the relevant concepts through examples and homework. The course covers elementary concepts from probability theory and statistics such as the basic rules of probability, random variables, distributions, expected values, independence, correlations and estimation. Simple models (such as the Binomial and the Poisson models) are applied to real world problems in engineering and other fields.

Announcement

First class on Augst 23: Orientation.

Time and Place

According to the official Rice web page.
Tentatively: Tuesday Thursday 9:25-10:40 in Duncan Hall 1064.

Instructor

Dr. Rudolf Riedi
Duncan Hall 2082, 713 / 348 3020,
Office Hours: TBA
or by appointment

TBA

Topics

Basic Probability, axioms of probability, Bayes rule, Independent events
Random variables, distributions, expected values, Bernoulli Trials
Bivariate variables, multivariate distributions,  independent r.v., correlations
Generating functions, characteristic function
Midterm Homework (open-discussion)
Continuous random variables
Limits and convergence, Law of Large Numbers, Central Limit Theorem
Simple models with applications, Gaussian, Rayleigh, Poisson
Midterm EXAM (open-notes)
Estimation, mean, variance
Linear regression, model fitting
Reliability, Poisson model
Second EXAM (open-books)

Textbook

• J. R. Cogdell `Modeling Random Systems"

• The course will closely follow this book; it is available at the campus bookstore.
One copy of the book is "on reserve" at Fondren (2 hours at a time).
Amazon lists several used copies at a reduced price.
• H. Stark and J. Woods, `Probability, Random Processes, and Estimation Theory for Engineers'.
• E. Wong and B. Hajek, `Stochastic Processes in Engineering Systems'
Standard references on Probability Theory
• A. Papoulis, `Probability, Random Variables, and Stochastic Processes'
• W. Davenport, `Probability and Random Processes'
• W. Feller, `An Introduction to Probability Theory and Its Applications'
• P. Billingsley, `Probability and Measure'

20%  Homework
20%  QUIZ (late September)
30%  Midterm EXAM  (late October)
30%  Last EXAM  (late November)

Topics dealt with in class and reading assignment will be posted here.
 Topics covered reading [exercises] August 23 Orientation, Introduction to Probability Bernstein: "Against the Goods"

Homework
(tex-source and solutions restricted to Rice University)

 Homework sheet Due date (in class) Solutions Problem Set 1

Late Homework Policy

Homework is due at the beginning of class on the due date. After the due date, but before solutions are handed out, homework can be turned in for 50% credit. In this case, please slip your homework under the instructors's office door, or bring it to class. After solutions are handed out, 0% credit will be issued. You are encouraged to work in groups for homeworks but you will hand in your own solution which you are expected to understand.

Tests

 Quiz (20%) Due: TBA, tentatively late September in class (open notes) Test 1 (30%) Due: TBA, tentatively early Nov. Take home, 180 minutes, (open notes) Test 2 (30%) Due: TBA, tentatively last day of class. Take home, 3 hours (open books)

Honor System

Homework:
Homework are "open-discussion". This means the following:
Collaboration for homework is encouraged. Any source of information is admissible. However, each student hands in her/his own homework which expresses his/her own understanding of the solution. Simple copying from others does not qualify as "collaboration".

Tests:
The term "open notes" means that look-up in any self-compiled hand-written source of knowledge is permitted.
The term "open books" means that look-up in any passive source of knowledge is permitted.
No help of any kind is allowed. For instance, no communication is admissible which involves any intelligent entity ---human or artifical--- or any active source which is able to respond to questions.

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disabled Student Services in the Ley Student Center.
April 21, 2005.  Dr. Rudolf Riedi