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STAT 564/MATH 564 − Theory of Probability


Description: Probability spaces, random variables, weak law of large numbers, central limit theorem, various discrete and continuous probability distributions.
Prerequisite(s): Calculus through multivariable/vector calculus (at the level of MATH 125, MATH 129, MATH 223).

This course in the Theory of Probability studies probability theory at the post-calculus level. It is targeted to provide graduate students in statistics, biostatistics, mathematics, and related disciplines with the concepts of probability and the mathematical development of statistics, and to provide a foundation for further study in probability theory at both the master's and doctoral levels.

Fall 2012

The course will meet Tuesdays and Thursdays from 2:00 pm - 3:15 pm in Medical Research Bldg. (MRB) room 102.
The textbook is Duxbury's Statistical Inference, 2nd Edition (2002) by George Casella and Roger Berger. Additional online resources are available at the book's Student Companion Site.

Material covered in the 2012 offering of the course will include:

The course syllabus gives complete information.

Attendance

Students are expected to attend class. If important circumstances prevent this, it is the student's responsibility to find out what was covered in class, what was assigned for reading or homework, and what special announcements (if any) were made. "Excessive absence" in this class will be construed to be absence from more than 10 percent of the scheduled class sessions, whether excused or unexcused, and will be subject to Administrative Drop as per University policies.

Homework Assignments - Fall 2012

Homeworks are based on exercises from the textbook.

Homeworks are due as assigned. No exceptions.
These assignments are subject to revision with prior notice. 

           Textbook 
Date due   Chapter    Exercises
-------------------------------------------------
Sep. 13       1       1.1, 1.3, 1.8a, 1.11ab, 1.19, 1.26, 1.33, 1.35, 1.39, 1.40, 1.50, 1.54

Oct.  2       2       2.1a*, 2.1bc, 2.8a, 2.11a, 2.12, 2.17a, 2.24ab, 2.32, 2.33ac, 2.38

Oct.  4      1-2      Exam 1 
 
Oct. 18       3       1.27a, 2.28ab (Hint: see Exercise 2.26), 3.2a, 3.5, 3.7, 3.9a, 3.13a, 3.15,
                      3.16a, 3.22a, 3.24a, 3.28a, 3.32a(E[tj(X)] only)

Nov. 13       4       4.4, 4.9, 4.10a, 4.15, 4.24, 4.30a, 4.40b(assume 4.40a holds), 4.41, 4.45a,
                      4.63, 4.64a*, 4.64b, 3.46

Nov. 15      3-4      Exam 2
  
Dec.  4       5       5.3, 5.8a, 5.11(E[S] ≤ σ only), 5.13, 5.14b, 5.15, 5.16ab, 5.22, 5.24, 5.32,
                      5.34, 5.35

Dec. 12               Comprehensive Final Exam

* problem optional

Specialized Downloads - Fall 2012

  • Textbook Errata List.

  • Related Reading List.

  • Selected articles on negative moments/inverse moments:
          Peng, C.Y. (2008). The first negative moment in the sense of the Cauchy principal value. Statistics and Probability Letters 78, 1765-1774.
          Khuri, A., and Casella, G. (2002). The existence of the first negative moment revisited. American Statistician 56, 44-47.
          Piegorsch, W.W. and Casella, G. (1985). The existence of the first negative moment. American Statistician 39, 60-62.

    • Student Responsibilities


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