MTH451 Introduction to Probability and Statistics

University of Rhode Island         Fall 2007

Instructor: Lubos Thoma
Office: Tyler Hall 214
Tel: 874.4451
Email: thoma at

Class Schedule: TuTh 12.30pm--1.45pm, Kelley Hall 102  
Office hours: TuTh 2.30pm - 4.00pm, and by appointment

Printable syllabus:   postscript     pdf

Suggested problems:   postscript     pdf

Important dates:
        Exam 1:     Thursday October 11, in class.
        Exam 2:     Thursday November 15, in class.
        Final Exam:     Thursday December 13, 3.00pm - 6.00pm       Fall 2007 final exam schedule

Prerequisite:   MTH 243 (Multivariable Calculus) or equivalent.

Textbook:   I. Miller, M. Miller, John E. Freund's Mathematical Statistics with Applications, Seventh Edition, Pearson Prentice Hall, isbn 0-13-142706-7.

Description:   MTH 451 is an introduction to the mathematical theory of probability using calculus. Probability theory has a tremendous variety of applications in all the sciences, including the social sciences, business and economics, and provides the mathematical foundation for statistics. It uses a wide variety of mathematical techniques and concepts, especially elementary set theory, combinatorics, and calculus. A main goal of this course is that you will be able to read more advanced material on probability and its applications and go on to courses in mathematical statistics and stochastic processes.
The class is designed for an audience with quite diverse interests, for example:
  if you are an engineering, science, economics or business major, probability will be a basic part of your mathematical toolkit;
  if you are a secondary math education major, you will most likely need to take the Praxis content exam, which contains material on discrete mathematics and probability for which this course is great preparation;
  if you are interested in taking the actuarial exams, this course is absolutely fundamental. We will discuss problems similar to problems on the actuarial exams during the course. For information about careers in actuarial science see careers in actuarial science; actuarial exams.
  finally, probability theory is a fundamental discipline in mathematics itself and well as the foundation for all of statistics. It can be entertaining, enlightening and sometimes surprising.

Evaluation:   Your grade will be based on quizzes, two in-class exams, and a final. We will have bi-weekly quizzes. The quizzes will be based on the material covered in class and suggested problems which will not be collected. (Special assignments, which might include use of Maple, will be collected.) Quizzes cannot be made up, but your lowest quiz grade will be dropped. Makeup exams will be given only for serious illness or emergency, and these must be documented.
Exams will draw from material covered in class, that is, any theorem, proof, or example that we cover in class and any suggested problem is a possible material for the tests. There will be two in-class exams and a comprehensive final. Dates see above.

Grading:   Your grade will be based on your exam scores, final exam score, quiz grades.
     quizzes and assignments 25%
     in-class exams 20% each
     final 35%

Accommodations:   Students who require accommodations and who have documentation from Disability Services (874-2098) should make arrangements with me as soon as possible.

  1.   Work on the suggested problems and keep the solutions. In fact, challenging and varied problems are an essential part of the course. Review concepts and methods from calculus as needed. Find a study partner.
  2.   Read the book carefully. It is helpful to read sections before we talk about them in class.
  3.   Attend class to keep current, ask questions, and learn new topics. Also, attending class allows you to see what is emphasized.
  4.   Review and application of calculus concepts : An explicit learning goal of this course is to strengthen your facility with calculus, including integration techniques, multiple integrals, the fundamental theorem of calculus, and series. You should be prepared to consult your old calculus textbook when needed. You are encouraged to use Maple or something equivalent for homework problems as a way to check your calculus computations. Moreover, some exam questions will be specifically designed to test your skill in using and applying calculus ideas and methods.
  5.   Probability functions on Maple.