Math 727, Spring 2005
Probability Theory
A mathematical introduction to premeasure-theoretic probability. Topics include probability spaces, conditional probabilities and independent events, random variables and probability distributions, special discrete and continuous distributions with emphasis on parametric families used in applications, the distribution problem for functions of random variables, sequences of independent random variables, convergence of random variables and limit theorems of probability theory.
Text: Probability, A. F. Karr, Springer-Verlag, 1993
Prerequisite: MATH 123 and graduate standing or permission of the instructor.
Credit Hours: 3
Prerequisites for the Course
MATH 123 and graduate standing or permission of the instructor.
Lectures
Members of the class are expected to attend the lectures, which will be used to explain new material, to work typical examples and to answer some questions. The course will cover material from all of the chapters.
Homework
Homework assignments, and the dates on which they are due, will be given weekly. Assignments will be collected at the beginning of the lectures.
Examinations
- EXAM I: Tuesday, 7 March
- EXAM II: Tuesday, 11 April
- FINAL: Monday, 15 May
Grading System
- Your grade in this course will be determined on a point system.
- A maximum of 500 points can be accumulated as follows:
- Exam I = 50 points, Exam II = 50 points, Final Exam = 250 points
- Homework ( 50 ), Quizzes (50), Attendance and Participation (50 ) = 150 points
- Total = 500 points
Changes: The instructor reserves the right to modify the schedule announced in this bulletin if the conditions arise during the semester which make such changes desirable.
Chapter Topics
1 - 2 Set Theory and Probability
3 - 4 Random Variables and their Distribution
5 Moments and Characteristic Functions
6 Theorems of Probability
7 Introduction to Estimation Theory