ST422-001:  
Introduction to Mathematical Statistics II
Spring 2008



Course:

ST422-001 Introduction to Mathematical Statistics II

Time:

MW from 1:30 to 2:45 p.m.

Place:

210 Harrelson Hall

 

 

Instructor:

Tom Gerig

Email:

gerig@stat.ncsu.edu

Telephone

515-1901

Office:

218 Patterson Hall

Office hours:

By appointment

 

TA:

TBA  (tutorials)

Email:

TBA

Tutorials

TBA


TA:

Sudha Veturi  (grade homework and homework solutions)

Available:

Tuesdays 1:00 to 2:00 and Fridays 1:15 to 2:15 at 110 Bureau of Mines building

Email:

ycveturi@ncsu.edu


Class links: Homework assignments and lectures | Ask a question | Private tutors

Course prerequisites:  ST421 and MA242

WMSRequired text (WMS): Dennis D. Wackerly, William Mendenhall III, and Richard L. Schaeffer (2002).  Mathematical Statistics with Applications, 6th Edition. Duxbury Advanced Series. ISBN:0534377416

Optional solutions manual:  Dennis D. Wackerly, William Mendenhall III, and Richard L. Schaeffer (2002).  Student Solutions Manual for Wackerly/Mendenhall/Schaeffer's Mathematical Statistics with Applications, 6th Edition. Duxbury Advanced Series. ISBN:0-534-38236-3 Contains worked solutions to the odd-numbered problems in WMS.

Homework: Homework will be assigned and due as indicated on the homework and lecture page.  Unexcused late homework will not be accepted. The TA will grade homework and assign a score for each homework set. The final homework average will be computed after dropping the two lowest grades. 

Homework grading: The end grade for each homework set is on a 100 point scale.  The grade is calculated from two parts, completion and accuracy.  The completion portion assigns credit if an earnest attempt is made to solve the problem, and the accuracy portion assigns credit for a correct solution. Partial credit is assigned in each part.  The completion percentage is calculated by dividing the number of problems attempted by the number of problem in the homework assignment.  The accuracy percentage is calculated by dividing the number of problems answered correctly that do not have answers in the back of the book, by the number of problems in the homework assignment that do not have answers in the back of the book. The total score is the average of the completion and accuracy scores.

It is important to check the homework page often since it is updated regularly.

Examinations: Examinations will be closed book and closed notes.  However students will be permitted to bring one 8½ by 11 inch sheet of notes (both sides, any content) to each exam. The final exam will be cumulative.  Bring a calculator to all exams.

Old Examinations: Links to old examinations are provided (without solutions) in the table below. Because of differences in pacing, coverage and emphasis from semester to semester, these exam do not necessarily reflect the kind of questions that will be on this semester's exams.

Year

Previous Exams

2003

MT1 MT2 MT3 Final

2004

MT1 MT2

.

Final

2005

MT1 MT2 MT3 Final

2006

MT1

MT2

MT3 Final

2007

MT1

MT2

.

Final

2008

MT1

MT2

.

.



Exam schedule (subject to change):

DATE
COVERAGE
Midterm exam 1
Wednesday, February 13
Sections 6.7, 7.1 to 7.3, 7.5, 7.6, 8.1 to 8.7
    __________________
Midterm exam 2
Monday, March 24
Sections 8.8, 8.9, 9.1 to 9.4, 9.6, 9.7, 9.9  plus material presented on mvue.
    __________________
Final exam
Wednesday, April 30
1:00-4:00 p.m.
Material on MT1 and MT2 plus Sections 10.1 to 10.12

Asking questions: If you have questions about lectures, homework assignments, exams, procedures or any other aspect of the course please log onto http://courses.ncsu.edu/ , follow the links to "ST" and "ST422" 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.

email you send to me:  Because I receive so much spam with my email I sometimes miss email messages from students.  Before I delete my spam messages I will search the subject line for "ST421", so when you write to me please include this in your subject line.

Anonymous mail: If you wish to send me an anonymous suggestion or reminder, send email to st422-001-comments@wolfware.ncsu.edu. The system will remove mail headers, but you must remember to removes your signature and other identifying information.

Grading System:  Final grade will be based on:

Final Semester Score = (HW + M1 + M2 + 2*F)/5

where HW is the homework average (out of 100) after dropping the two lowest scores and M1, M2, and F are the scores (out of 100) on the three midterm exams and the final exam. Grades will be assigned on the ± scale according to this grading scale.

On-line grade book: I will record your homework and examination scores in the ST422 Grade Book as they become available.  Please check these from time to time and let me know if the posted scores differ from those in your records.  Note that the scores posted on the Grade Book are not official. 

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 NCSU Code of Student Conduct and Procedures. For a more thorough 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 Office (DSO), 1900 Student Health Center, CB# 7509, 515-7653.

Reference handouts: Mathematical formulae    Discrete distribution    Continuous distributions
                               Table 8.1

Software:
 StaTable is a program that provides probability calculations for 25 common probability distributions.  Numerical calculations may be obtained for tail areas (e.g. cdf) and for percentage points of selected discrete and continuous distributions.  The program is provided at no cost by Cytel.  A free download version is offered for Windows.

Printing Handouts: Instructions for greatly speeding up the printing of the lecture slides:
  • Click the icon for the lecture handout you wish to print.  The slides will appear in Adobe Acrobat.
  • Click on File > Print.  This will bring up the Print window.
  • Click on the Advanced button (located at the bottom left-hand-side of the Print window).  This will bring up the "Advanced Print Setup" window.  Check the "Print As Image" box (located near the top in the center of the "Advance Print Setup" window).  Click on OK to return to the Print window.
  • To select between Portrait and Landscape orientation, click on Properties.  Landscape is preferred
  • Click OK to start printing.
Information provided on this webpage is subject to change so students should refer back to it periodically.

Reference material
:

General:

Elliot A. Tanis and Robert V. Hogg (2008).  A Brief Course in Mathematical Statistics.  Prentice Hall.

Jay L. Devore and Kenneth N. Berk (2007).  Modern Mathematical Statistics with Applications. Thomson Brooks/Cole.

John A. Rice (2007). Mathematical Statistics and Data Analysis, 3rd Edition. Thomson Brooks/Cole.

Richard J. Larsen and Morris L. Marx (2006).  An Introduction to Mathematical Statistics and Its Applications, 4rd Edition.  Prentice Hall.

Robert V. Hogg and Allen T. Craig (2005).  Introduction to Mathematical Statistics, 6th Edition. Prentice Hall.

Asha Seth Kapadia, Wenyaw Chan and Lemuel Moye (2005).  Mathematical Statistics with Applications.  Chapman & Hall.

Michael J. Evans and Jeffrey S. Rosenthal (2004).  Probability and Statistics - The Science of Uncertainty. W. H. Freeman & Co.  

Irwin Miller and Marylees Miller (2004).  John E. Freund's Mathematical Statistics with Applications, 7th Edition. Prentice Hall College Division.  (QA276.M426 2004) 

Larry Wasserman (2004).  All of Statistics: A Concise Course in Statistical Inference. Springer Verlag.  (QA276.12.W37 2004) 

Steven F. Arnold (1990). Mathematical Statistics  Prentice-Hall.  (QA276.A74 1990) 

Alexander McFarlane Mood, Duane C. Boes, Franklin A. Graybill (1974).  Introduction to the Theory of Statistics, 3rd Edition. McGraw-Hill Higher Education.  (QA276.M67 1974) 

Bayesian Methods:

William M. Bolstad (2004). Introduction to Bayesian Statistics  Wiley Interscience.

Jeff Gill (2002). Bayesian Methods: A Social and Behavioral Sciences Approach  CRC Press.

Simulation and Bootstrapping:

Michael R. Chernick (1999). Bootstrap Methods: A Practitioner's Guide  Jossey-Bass Wiley.

Christopher Z. Mooney (1997). Monte Carlo Simulation  Sage Publications, Inc.

Course objectives:  

A prime objective of the ST421-2 course sequence is to present techniques and basic results of probability and mathematical statistics at a rigorous, but not advanced level.  In ST421 we develop the probabilistic tools and language of mathematical statistics. The course describes probabilistic models for and properties of random variables and vectors, common probability distributions, and large sample results. In the second semester course, ST422, 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.  ST421-2 is a required sequence for undergraduates majoring in Statistics and for Ph.D. students minoring in Statistics.  A related sequence, ST521 and ST522, presents similar material at the advanced calculus level.

Syllabus:  In ST422 we shall cover most, but not all of the material in chapters 8 through 11 of WMS. We shall supplement this material with lectures on Bayesian inference.
  • Sampling distributions related to the normal: mean, chi-square, student-t, F; the central limit theorem.

  • Parameter estimation - introduction and properties, point estimators; bias and mean squared error; interval estimators; sample size determination; relative efficiency, consistency.

  • Parameter estimation - classical approaches: minimum variance unbiased estimation, method of moments, maximum likelihood; sufficiency.

  • Parameter estimation - Bayesian approaches: prior and posterior probability, point and interval estimation using the posterior, choosing a prior.

  • Hypothesis testing - formal testing paradigm, properties of tests, p-values. Common normal theory tests, large sample tests. Approaches to testing, most powerful alpha-level tests, likelihood ratio tests.