## STAT-331 Probability & Mathematical Statistics I

Mathematics, Statistics & Computer Science Department

COURSE NO./TITLE: STAT-331 (354-331) Probability & Mathematical Statistics I

CREDIT: 3

COURSE DESCRIPTION: Sample spaces. Probability functions for discrete and continuous sample spaces. Conditional probability and independence. Random variables; probability density and cumulative distribution functions; joint, marginal, and conditional distributions. Expected values, moments, and moment generating functions. Binomial, hypergeometric, poisson, normal, and gamma distributions.

Prerequisites: MATH-154 or MATH-157, completion of, or concurrent enrollment in, MATH-158 is highly recommended.

TEXTBOOK:

• Intro to Mathematical Statistics & Its Applications, 4th Ed. by Marx (F07)
• (Adopted 8/01: Introduction to Mathematical Statistics & Its Applications, 3rd Ed. by Marx
• (Prior to Fall 01: Probability & Statistical Inference, 5th Ed., by Hogg & Tanis)
• (Prior to Fall 97: Mathematical Statistics & Data Analysis, 2nd Ed., by Rice)
• (Prior to Fall 95: Introduction to Mathematic Statistics, 2nd Ed., by Larsen)

COURSE OBJECTIVES: The course will enable students to:

1. Explain the relationship between probability and statistics and the importance of each.
2. Demonstrate an understanding of the basic principles of probability.
3. Use the properties of discrete and continuous random variables with their joint, marginal, and conditional distributions.
4. Use the various families of probability distributions to model various types of data.
5. Demonstrate skills in problem solving by writing of clear, complete, logically correct solutions.
6. Use a statistical computing package, such as SPSS or STATGRAPHICS.

COURSE OUTLINE:

1. Introduction: The Meaning of Probability
2. Probability
A. The Sample Space and Events; The Algebra of Sets
B. Discrete and Continuous Probability Functions
C. Conditional Probability, and Independence; Bayes' Rule
D. Combinatorics, Combinatorial Probability
3. Random Variables
A. Densities and Distributions
B. Joint, Marginal and Conditional Densities
C. Independent Random Variables
D. Combining and Transforming Random Variables
E. Order Statistics
F. Expected Values, Variance, and Higher Order Moments
G. Moment Generating Functions
H. Chebyshev's Inequality
4. Common Probability Distributions
A. The Poisson Distribution
B. The Normal Distribution
C. The Binomial, Geometric and Negative Binomial Distributions
D. The Hypergeometric Distribution
E. The Gamma Distribution Revised 8/07