ST 521-001:
Statistical Theory I
Fall Session, 2007


ST 521-002 Statistical Theory I
(ST 521L-202 Statistical Theory Lab)


MWF from 11:20 a.m. to 12:10 p.m.
(W from 12:25 - 1:15 p.m.)


320 Harrelson Hall




Sujit Ghosh





220C Patterson Hall

Office hours:

Wednesday, 3:00 - 5:00 p.m. or by appointment

. .


Anna Burkhart and Mihye Ahn

Emails: and




Statistics Tutorial Center, 009 Patterson Hall

Office hours:

A. Burkhart (Tue 3:00-5:00) and M. Ahn (Mon 2:00-4:00)

Class links: Lectures & Assignments| Ask a question | Private tutors

Course corequisite: (MA 425 or MA 511) and MA 405

Required text: Casella G. and Berger R. L. (2002). Statistical Inference, 2nd Edition. Duxbury Advanced Series. (ISBN: 0534243126)

Errata for the text: Download this Errata

Statistical Resources: Statistical Java Applications

Homework: Homework will normally be assigned weekly (as indicated on the homework page) at the end of class each Wednesday. Homework solution will normally be discussed during the Lab hours on Wednesdays. Unexcused late homework will not be accepted. The final homework average will be computed after dropping the two lowest grades.

Examinations: Examinations will be closed book and closed notes. However students will be permitted to bring one 81/2 by 11 inch sheet of notes (both sides) to the midterm exam and two to the final exam. The final exam will be cumulative, but weighted towards the materials covered after the midterm. You may bring calculators to all exams, in addition to pen/pencil and scratch papers.

Exam schedule:
Midterm exam
Wednesday, October 10
11:30-1:00 p.m.
Chapters 1-2
Final exam
Monday, December 14
8:00-11:00 a.m.
Chapters 1-5

Asking questions: If you have questions about lectures, homework assignments, exams, procedures or any other aspect of the course please log onto, follow the links to "ST" and "ST521" and click on "Message Board". Then click on "Post New Topic", enter your question in the Message box, and click on "Submit Message". You will receive a response from me or another student. Everyone in the class will be able see your question and the response.

Anonymous mail: If you wish to send me an anonymous suggestion or reminder, click here. The system will remove mail headers, but you must remember to remove your signature and other identifying information.

Grading System: Final grade will be based on:

Final Semester Score = (2.0xHW + 3.5xM + 4.5xF)/10

where HW is the homework average (out of 100) after dropping the two lowest scores and M and F are the scores (out of 100) on the midterm and the final exam. Grades will be assigned on the +/- scale.

Auditing: Auditors are expected to attend class regularly and submit homework on the same schedule as the other students. The final grade for auditors (AU or NR) will be based on their final homework average. A homework score of 75 or better is required for an AU.

Policy on Academic Integrity: The University policy on academic integrity is spelled out in Appendix L of the NCSU Code of Student Conduct. For a more though elaboration see the NCSU Office of Student Conduct website. For this course group work on homework is encouraged. However copying someone else's work and calling them your own is plagiarism, so the work you turn in should be your own.

Students with Disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students (DSS), 1900 Student Health Center, CB# 7509, 515-7653.

Online Class Evaluation: Online class evaluations will be available for students to complete during the last two weeks of class (November 26-December 9). All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.
Click Online evaluation. More information at ClassEval

Reference material (Have requested these be on reserve at DH Hill Library):

Bickel, Peter J. and Docksum, Kjell A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Vol I, 2nd Edition. Prentice Hall.

DeGroot, Morris, H. and Schervish, Mark, J. (2001). Probability and Statistics, 3rd Edition. Addison Wesley.

Evans, Michael, J. and Rosenthal, Jeffrey, S. (2004). Probability and Statistics: The science of uncertainty. W. H. Freeman & Company.

Robert V. Hogg and Allen T. Craig (1994). Introduction to Mathematical Statistics, 5th Edition. Prentice Hall.

Rohatgi, Vijay K. (2003). Statistical Inference (paperback). Courier Dover Publications.

Ross, Sheldon (2006). A First Course in Probability. Prentice Hall.

Course objectives:

A prime objective of the ST521-2 course sequence is to present techniques and basic results of probability and mathematical statistics at a rigorous and advanced calculus level.

In ST521 we develop the probabilistic tools and language of mathematical statistics. The course describes probabilistic models for and properties of random variables, common probability distributions, and large sample results. In the second semester course, ST522, the structure of statistical inference procedures is studied. In particular, the theory of estimation, confidence sets, hypothesis testing, and prediction for common parametric models are investigated.

Students taking the course will have completed three semesters of calculus and had some exposure to basic probability and statistics. ST521-2 is a required sequence for Masters students majoring in Statistics and for Ph.D. students minoring in Statistics. A related sequence, ST793-4, presents similar material at the advanced measure-theoretic level.

Syllabus: In ST521 we shall cover most, but not all of the material in chapters 1 through 5 of Casella & Berger.
  1. Probability Theory: axiomatic foundations, conditional probability, random variables, probability distributions.
  2. Transformations and Expectations: functions of random variables, expected values, moment generating functions.
  3. Families of Distributions: discrete and continuous distributions, exponential family, location and scale family.
  4. Random Vectors: joint, marginal and conditional distributions, hierarchical and mixture models, covariances.
  5. Sampling Distributions and Convergence: random samples, sums of random variables, convergence concepts.
(roughly three weeks will be devoted to each of the above topics)

Last updated on: August 16, 2007