2005 Fall MATH 135-01
Bulletin Course Description Probability models, random variables with discrete and continuous distributions. Independence, joint distributions, conditional distributions. Expectations, functions of random variables, central limit theorem. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title PROBABILITY Department MATH Course Number 2005 Fall 135 Section Number 01 Primary Instructor Huber,Mark Prerequisites Prerequisite: Mathematics 102, 103, or 105. Course Homepage courses.duke.edu
Prerequisites
Mathematics 103. Mathematics 104 is helpful but is not a prerequisite.
Synopsis of course content
The course starts with the marbles in jars level of probability, but by the end we'll have explored a wide variety of topics in modern probability. Many people have seen continuous distributions in the form of normal (aka Gaussian, aka bell-curve) distributions. In addition to normals, we'll study uniforms, exponentials, gammas, betas, and Cauchy distributions. Discrete distributions tackled include Bernoulli, binomial, Poisson, geometric and negative binomial. A large part of the course will be the concept of conditioning: how probabilities change when additional information is introduced into a system. Also tackled are topics such as expectation and standard deviation and important theorems such as the Strong Law of Large Numbers and the Central Limit Theorem.
Textbooks
Probability, Jim Pitman
ISBN 0387979743
and
Schaum's Outlines Probability 2nd Edition, Seymour Lipschitz
ISBN 0071352031
Assignments
A homework assignment will be due every Wednesday (except when breaks or midterms interfere). The lowest homework grade will be dropped. You may work on this with other people, and are encouraged to do so, provided you acknowledge this when you hand it in.
Exams
There will be two midterms and a final exam. The midterms will be in class, and for each you will be allowed to use a page of notes that you write up. For the final you will be allowed two pages. Other than those pages, the tests are closed book. The final will be cumulative.
Term Papers
There will be no term papers.
Grade to be based on
Homework: 20%
Midterm 1: 20%
Midterm 2: 20%
Final: 40%
