CATALOG DESCRIPTION:

1702.360 Introduction to Probability and Statistics I                                                         3 s.h.
(Prerequisites: 1701.131 Calculus II and 1701.150 Discrete Math, or permission of instructor)

An introduction to the theory and application of mathematical statistics at the post-calculus level. After a brief introduction to the concepts of descriptive statistics, the emphasis is on probability theory and its applications. Topics covered include sample spaces, random variables, discrete and continuous probability distributions, mathematical expectation, and multivariate distributions.  Use of a graphing calculator is required.

OBJECTIVES:

Students will gain skills in using the theory of probability, combinatorics, and probability distributions to model applications.  They will be able to recognize and apply many discrete and continuous probability distributions.  They will derive and use moment generating functions, and study discrete and continuous random variables in enough depth to prepare them for the study of the Central Limit Theorem in Probability and Statistics II.
 

CONTENT:

1. Descriptive Statistics

2. Elementary Probability

 2.1 Axiomatic approach
 2.2 Combinatorics
 2.3 Probability theorems
 21.4 Bayes' theorem

3. Discrete Probability Distributions

 3.1 Discrete random variables
 3.2 Expected values of a random variable and functions of a random variable
 3.3 Binomial distribution
 3.4 Geometric and negative binomial distributions
 3.5 Hypergeometric distribution
 3.6 Poisson distribution
  3.7 Moment generating functions

4. Continuous Probability Distributions

 4.1 Continuous random variables
 4.2 Expected values of a random variable and functions of a random variable
 4.3 Uniform distribution
 4.4 Normal distribution
 4.5 Gamma and exponential distributions
 4.6 Beta distribution
 4.7 Moment generating functions.

5. Multivariate Probability Distributions

 5.1 Multivariate distributions
 5.2 Marginal and conditional distributions
 5.3 Independent random variables
 5.4 Expected values for functions of random variables
 5.5 Covariance and correlation
 5.6 Linear Functions of random variables
 

POSSIBLE TEXTS:

*D. D. Wackerly, MATHEMATICAL STATISTICS WITH APPLIC. (free student solutions manual), Duxbury, 6th edition

Berry, Donald A., and Bernard W. Lindgren, Statistics: Theory and Methods, 2nd edition.  Duxbury/Wadsworth, Belmont, CA, 1996.

Hastings, Kevin J., Probability and Statistics.  Addison-Wesley Longman, Reading, MA, 1997.

Hogg, Robert V., and Elliot A. Tanis, Probability and Statistical Inference, 6th edition. Prentice-Hall, Upper Saddle River, NJ, 2000.

*Larsen, Richard J., and Morris L. Marx, An Introduction to Mathematical Statistics and Its Applications, 3rd edition.  Prentice-Hall, Upper Saddle River, NJ, 3rd Edition

Wackerly, Dennis D., William Mendenhall III, and Richard L. Scheaffer, Mathematical Statistics with Applications, 5th edition, Duxbury/Wadsworth, Belmont, CA, 1996.