STATE UNIVERSITY COLLEGE AT BUFFALO
Department of Mathematics

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 events
 2. Axioms and elementary theorems
 3. Conditional probability
 4. Independence
 5. BayesÕ Theorem
B. Probability Distributions
 1. Discrete and continuous random variables
 2. Probability distributions and densities
 3. Multivariate distributions and densities
 4. Marginal and conditional distributions and densities
C. Mathematical Expectation
 1. Expected value of a random variable
 2. Moments, mean and variance
 3. ChebyshevÕs theorem
 4. Moment-generating functions
 5. Product moments and covariance
 6. Means and variances of linear combinations
D. Special Probability Distributions and Densities
 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.