MATH 4343 - Trindade

MATH 4343 -- Mathematical Statistics II -- Spring 2010

The sequence MATH 4342-4343 develops the basic mathematical theory of statistical inference at an undergraduate level. Three semesters of calculus are prerequisite for this sequence (MATH 2350). MATH 4342 introduces the concepts and methods of probability and distribution theory. In MATH 4343, these tools are used to develop the theory of statistical estimation and hypothesis testing. MATH 4342 is a prerequisite for MATH 4343.

Instructor

Dr. Alex Trindade, 211 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu; Phone: 742-2580 x 233.
Course Meets: 14:00-14:50 MWF, in Math 110.
Office Hours: 11:00-12:00 MWF, or by appointment.

Text Books

Required: Mathematical Statistics with Applications, 7th ed., by Wackerly, Mendenhall, and Scheaffer, Duxbury Press, 2008. (Link to companion website.)
Recommended: Accompanying Students' Solutions Manual to odd problems (ISBN-13: 978-0-495-38506-6). Available from the publisher: 1-800-423-0563.

Topics to be Covered

Chapters 7-10 of the book: sampling distributions; the central limit theorem; point and interval estimation; properties of point estimators; methods of estimation; hypothesis testing.

Expected Learning Outcomes

After completing this course the student should be able to:

Calculate probabilities and quantiles for sampling distributions related to the normal distribution (t, chi-square, F); apply the central limit theorem to calculate probabilities and quantiles for the sample mean.
Construct point and interval estimators; evaluate their goodness (bias, variance, mean squared error).
Determine properties of point estimators (efficiency, consistency, sufficiency); find minimum variance unbiased estimators; find method of moments and maximum likelihood estimators.
Perform hypothesis tests for the mean; compute p-values, type I, and type II errors; determine the power of a test and apply the Neyman-Pearson Lemma; construct likelihood ratio tests.

Methods of Assessing the Expected Learning Outcomes

The course grade will be determined from homeworks, tests, and a comprehensive final exam, weighted as follows.

Weekly homework problems (10%).
Test 1, Week of Feb 8-12 (20%).
Test 2, Week Mar 8-12 (20%).
Test 3, Week Apr 12-16 (20%).
Final Exam, comprehensive (30%): Monday May 10, 7:30 - 10:00 am.

Course averages of at least 90%, 80%, 70%, and 60% will guarantee letter grades of A, B, C, D, respectively. Grades will be posted on your eLearning tab, accessible through raiderlink.

Homework Problems

In order to master the course material it's essential to work as many exercises as possible. The following list gives the minimum number of problems that you should do. Starred (*) problems will be collected for grading every friday (except on test weeks), and will be announced the previous friday. Start each question on a separate page and staple everything together. No late homeworks will be accepted.

Section 7.1: 6, 8.
Section 7.2: 13, 21, 25*, 29, 31, 33*, 37, 38*.
Section 7.3: 42*, 49*, 51, 55*.
Section 7.5: 73*, 74*, 75, 77*, 79, 85.
Section 8.2: 5*, 6*, 9*, 11, 13, 15.
Section 8.4: 23*, 27, 28*, 35*, 37.
Section 8.5: 39*, 41, 43*, 45, 46*.
Section 8.6: 55, 56*, 61*, 63, 65*.
Section 8.7: 70, 71*.
Section 8.8: 80*, 83*, 87, 91*, 92.
Section 8.9: 95*, 102.
Section 9.2: 1*, 2, 3, 4*, 5*, 6.
Section 9.3: 15*, 16, 21, 24*, 25*, 32.
Section 9.4: 37*, 38*, 42, 43*, 45*, 49.
Section 9.5: 56*, 59*, 60, 61, 63*.
Section 9.6: 69*, 71*, 73, 74*, 75.
Section 9.7: 80, 81*, 82, 83, 88*, 97*.
Section 9.8: 98*, 100, 102*.
Section 10.2: 2*, 3, 5.
Section 10.3: 9, 17, 20*, 27, 32*.
Section 10.5: 46, 47*.
Section 10.6: 51*, 52, 57*.
Section 10.8: 64*, 67, 68, 71, 73*.
Section 10.9: 79*, 80, 83, 84*.
Section 10.10: 89, 91, 93, 95, 99.
Section 10.11: 105, 106, 107, 111.

Other Policies

In the unlikely event that you have to miss a test due to:

illness/personal/family matters, you must inform me in advance and provide a written excuse from the Center for Campus Life;
officially sanctioned University trips (e.g. sports), you must inform me in advance and provide a letter from the sponsoring department.

Academic Integrity is assumed and is expected at all times. Academic dishonesty, of which the most serious offence is cheating on tests, will not be tolerated. Students are advised to acquaint themselves with the Code of Student Conduct.

It is the aim of the faculty of Texas Tech University to foster a spirit of complete honesty and a high standard of integrity. The attempt of students to present as their own any work that they have not honestly performed is regarded by the faculty and administration as a serious offense and renders the offenders liable to serious consequences, possibly suspension.

Continuous formative assessment of the progress of the course will occur via ongoing communication between the instructor and the students. To this end, all students are encouraged to ask questions during class, and to seek the instructor's help out of class when needed.

Finally, remember that final grades are final. Care about your grade continuously during the semester. After the final exam it is too late!!!

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