I. Number and title of course

MAT 382-Topics in Mathematical Statistics

II. Reasons for addition to present curricula

A. To make available to those majoring in mathematics, and to others with the prerequisites, a study of topics in the important area of mathematical statistics.

B. To provide those who are preparing to teach mathematics in the secondary schools with an opportunity to deepen their understanding of the field of mathematical statistics.

C. To provide an important elective course for the mathematical sciences program.

A. To develop several important areas of statistics on a mathematically sound basis.

B. To present a clear and precise understanding of the methods and tools of statistical inference.

C. To show the usefulness of statistical theory by a variety of examples and applications.

(A) Special discrete and continuous distributions

1. Negative binomial and geometric

2. Hypergeometric

3. Gamma and chi-square

4. Beta

5. t and F

6. Multinomial and multivariate hypergeometric

7. Bivariate normal

1. Distribution function technique

2. Transformation of variable technique

3. Moment-generating function technique

1. Properties of estimators: unbiasedness, efficiency, consistency and sufficiency.

2. Method of moments

3. Method of maximum likelihood

1. The Neyman-Pearson Lemma

2. Power function of a test

3. Likelihood ratio tests

1. The method of least squares

2. Normal regression analysis

3. Normal correlation analysis

1. One-way designs

2. Two-way designs

(H) Nonparametric methods

V. Bibliography, tests, and readings

A. Brunk, H.D., An Introduction to Mathematical Statistics, Lexington: Xerox College Publishing, third edition: 1975.

B. Canavos, G.C., Applied Probability and Statistical Methods, Boston: Little, Brown and Company, 1984.

C. Cochran, W. G., Sampling Techniques, New York: John Wlley & Sons, Inc.,third edition: 1977.

D. Draper, N.R. and Smith, H., Applied Regression Analysis, New York: John Wiley & Sons, Inc., second edition: 1981.

E. Freund, J.E. and Walpole, R.E., Mathematical Statistics, Englewood Cliffs: Prentice-Hall, Inc., third edition: 1980.

F. Hoel, P.G., Introduction to Mathematical Statistics, New York: John Wiley & Sons, Inc., fifth edition: 1984.

G. Hogg, R.V. and Tanis, E.A., Probability and Statistical Inference, New York: Macmillan Pub. Co., Inc., second edition: 1983.

H. Larsen, R.J. and Marx, M.L., An Introduction to Mathematical Statistics and Its Applications, Englewood Cliffs: Prentice-Hall, Inc., 1981.

I. Lindgren, B.W., Statistical Theory, New York: Macmillan Publ. Co., Inc., third edition: 1976.

J. Mood, A.M., Graybill, F.A., and Boes, D.C., Introduction to the Theory of Statistics, New York: McGraw-Hill Book Company, third edition: 1974.

K. Walpole, R.E. and Myers, R.H., Probability and Statistics for Engineers and Scientists, New York: Macmillan Pub. Co., Inc., second edition: 1978.

A. Both lectures and discussions will be used in the presentation of the material. An effort will be made to have the students acquire as much of the material as possible through their own reading and study so that class time can be devoted to clarification of points which prove difficult for them, to expansion of parts which may be of particular interest to the class, and to presentations by the students of the results of their own efforts. Exercises will be provided which involve the entire mathematical development of the topics with which they are associated.

B. Evaluation will be related to the objectives of the course and will be made by means of written examinations (class and/or "take-home") and reports made in class on the assignments.

MAT 263 and MAT 381.

VIII. Credit

Three semester hours.

IX. Statement of approval

This revised course proposal was examined in accord with recommended procedures and has been approved by the Mathematics Department on

(Date) _____ ______________________ (Department chairperson)

X. Catalog description

MAT 382 TOPICS IN MATHEMATICAL STATISTICS

Topics selected from: Special distributions, Distribution theory, Estimation, Hypothesis testing, Regression and Correlation, Analysis of Variance, Sample surveys and Nonparametric methods.

XI. Statement of qualifications of faculty who will teach the course.

All members of the Department of Mathematics having interest and experience in Probability Theory and Mathematical Statistics.

XII. Support services required

A classroom with sufficient light, proper temperature, room for classroom activity, and plenty of chalkboard space.