Course Revision
I. Number and Title of Course
MAT 381 Probability
II. Reasons for Revision
We have updated the bibliography to better address and reflect the current work in this area, and we have redefined the major objectives in terms of student outcomes. The course continues to serve the following purposes in our program:
A. To make available to those majoring in mathematics, and to others with the prerequisites, the fundamentals of probability theory.
B. To provide those who are preparing to teach mathematics in the secondary schools with the appropriate background to teach probability.
C. To provide an important course for our mathematics programs.
III. Major Objectives of the Course
A. Students will develop a mathematical foundation in the area of probability.
B. Students will gain a working undertsanding of the basic theorems of probability.
C. Students will be able to relate the mathematical theory of probability
to applications in the real world.
IV. Topical Outline
A. Probability Models
1. Sample spaces and eventsB. Probability Distributions
2. Axioms and elementary theorems
3. Conditional probability
4. Independence
5. BayesÕ Theorem
1. Discrete and continuous random variablesC. Mathematical Expectation
2. Probability distributions and densities
3. Multivariate distributions and densities
4. Marginal and conditional distributions and densities
1. Expected value of a random variableD. Special Probability Distributions and Densities
2. Moments, mean and variance
3. ChebyshevÕs theorem
4. Moment-generating functions
5. Product moments and covariance
6. Means and variances of linear combinations
1. Discrete and continuous uniform
2. Bernoulli and binomial
3. Negative binomial and geometric
4. Hypergeometric and Poisson
5. Multinomial and multivariate hypergeometric
6. Gamma, exponential and chi-square
7. Beta
8. Normal and its approximation to the binomial
V. Bibliography
Aunon, Jorge I. and Chandrasekar,
V. Introduction to Probability and
Random Processes. New York, N. Y.:
WCB/McGraw-Hill Pub. Co., 1997.
Berry, Donald A. and Lindgren,
Bernard W. Statistics: Theory and
Methods. Pacific Grove, Calif.: Brooks/Cole Pub.
Co., 1990.
Freund, John E. Mathematical
Statistics (5th edition). Englewood
Cliffs, N. J.: Prentice-Hall, Inc., 1992.
Freund, John E. Introduction
to Probability. Mineola, N. Y.: Dover
Publications, Inc., 1993.
Ghahramani, Saeed. Fundamentals
of Probability. Englewood Cliffs, N.
J.: Prentice-Hall, Inc., 1996.
Hastings, Kevin J. Probability
and Statistics. Reading, Mass.: Addison-Wesley
Pub. Co., 1997.
Helms, Lester L. Probability
Theory with Contemporary Applications.
New York, N. Y.: W. H. Freeman and
Co., 1997.
Hogg, Robert V. and Craig, Allen
T. Introduction to Mathematical Statistics
(5th edition). Englewood Cliffs, N.
J.: Prentice-Hall, Inc., 1995.
Hogg, Robert V. and Tanis, Elliott
A. Probability and Statistical Inference
(5th edition). Englewood Cliffs, N.
J.: Prentice-Hall, Inc., 1997.
Kelly, Douglas G. Introduction
to Probability. Englewood Cliffs, N.
J.: Prentice-Hall, Inc., 1994.
Larson, Harold J. Introduction
to Probability. Reading, Mass.: Addison-Wesley
Pub. Co., 1995.
Lindgren, Bernard W. Statistical
Theory (4th edition). New York,
N. Y.: Chapman and Hall, 1993.
Olkin, Ingram; Gleser, Leon and
Derman, Cyrus. Probability Models and
Applications (2nd edition). Englewood
Cliffs, N. J.: Prentice-Hall, Inc., 1994.
Rice, John A. Mathematical
Statistics and Data Analysis (2nd edition).
Belmont, Calif.: Wadsworth Pub. Co., 1995.
Ross, Sheldon M. A First
Course in Probability (5th edition).
Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1998.
Scheaffer, Richard L. Introduction
to Probability and Its Applications (2nd
edition). Belmont, Calif.: Wadsworth Pub. Co.,
1995.
VI. Presentation and Evaluation
A. Both lectures and discussions will be used in the presentation of the material. Exercises will be provided which involve the entire mathematical development of the topics with which they are associated and also demand intuitive appreciation of the material.
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/or
reports made in class on the assignments.
VII. Prerequisites
MAT 270 and either MAT 127 or MAT 162.
VIII. Credit
3 credits: (3:0)
IX. Departmental Approval
This course proposal was examined in accordance with recommended procedures
and
approved by the Department of Mathematics Curriculum Committee on
_____________________. _____________________________________
Signature of Department Chair Date
X. Catalog Description
Probability models, discrete and continuous random variables and their
distributions or densities, multivariate distributions, mathematical expectation,
and special distributions anddensities.
XI. Qualifications of Faculty who will teach the course
A. General faculty qualifications: An M.S. or M.A. in Mathematics or a related area and expertise in the area of probability.
B. Some of the faculty who havethe necessary qualifications at the present
time are:
John Slivka, Ph.D. in Mathematics
XII. Support Services Required
Present classroom facilities are adequate.