STAT 712

Mathematical Statistics I

Fall 2002

Location: LeConte 210B

Time: MW 2:30 - 3:45 p.m.

Instructor: W. J. Padgett

E-mail: padgett@stat.sc.edu

Description:

Mathematical Statistics I (3) (Prereq: Advanced calculus or consent of instructor) Sample spaces, probability and conditional probability, independence, random variables, expectation, distribution theory, sampling distributions, laws of large numbers and asymptotic theory, order statistics, and estimation.

Purpose of Course:

To acquaint beginning graduate students in statistics and other disciplines with the concepts of probability and mathematical development of statistics. To provide a foundation for further study in probability theory and statistical theory at both the master's and doctoral levels.

Current Textbook:

A COURSE IN MATHEMATICAL STATISTICS, 2nd Edition, George G. Roussas, Academic Press, 1997.

Topics:

                                                            
   Probability:  (Chapters 1-2)                             August 26 - September 9 
      Sample spaces; events; axioms and laws of probability;
      independence; conditional probability; Bayes' Theorem.
   Random Variables and Vectors:  (Chapters 3-4)            September 11 - 25
      Discrete and continuous random variables and vectors;
      distribution functions; densities; joint, marginal, 
      and conditional distributions; specific parametric 
      distributions.
   EXAM 1                                                   September 30  
   Expectation, Moments, Generating Functions:  (Chapters 5-6)
      Moments; probability inequalities for random          October 2 - 23  
      variables; characteristic and generating functions.
   Independent Random Variables and Convergence:  (Chapters 7-8)
      Modes of convergence; laws of large numbers;          October 28-November 6  
      central limit theory; Slutzky's theorem.
   EXAM 2                                                   November 11  
   Transformations of Random Variables:  (Chapter 9-10)     November 13 - 25  
      Application to order statistics, chi-square, t, 
      and F distributions.
   Introduction to Estimation:  (Part of Chapter 11)        December 2 - 4  

   FINAL EXAM                                               December 14  
                                                            (Saturday, 2:00 p.m.)

(STAT 713 will begin with Chapter 11 of the textbook.)

Homework: Approximately 6-8 homework sets will be assigned and turned in for grading. You are to do these as assigned teams, turning in one paper per team with all team members contributing. Assigned exercises are to be done but not turned in--you are encouraged to work together on them. You also might be called upon (randomly, of course) to write solutions to some of the exercise problems on the blackboard from time to time.

Grading: The final semester grade will be determined by the weighting:

Tests 1 and 2 - 50%
Homework - 20%
Final Examination - 30%
The overall semester grading scale (percentage) will be:
At least 90% = A; 86-89% = B+; 80-85% = B; 76-79% = C+; 70-75% = C; etc.

Some Similar Textbooks:

Introduction to Mathematical Statistics, R.V. Hogg and A.T. Craig
Statistical Inference, G. Casella and R. Berger
Mathematical Statistics, S. Arnold
Introduction to the Theory of Statistics, Mood, Graybill and Boes
Mathematical Statistics, P. Bickel and K. Doksum
Statistical Theory, B. Lindgren

Office Hours: MW 1:00-2:30 p.m., TTh 10:30-11:30 a.m., or by appointment.