STAT-331 (354-331) Probability & Mathematical Statistics I. CREDIT: 3 ... (Prior to
Fall 97: Mathematical Statistics & Data Analysis, 2nd Ed., by Rice). (Prior to ...
Mathematics, Statistics & Computer Science
University of Wisconsin-Stout Jarvis Hall Science Wing 231 Menomonie, WI 54751-0790
COURSE NUMBER/TITLE:
STAT-331 [354-331] Probability & Mathematical Statistics I
CREDITS:
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 Calculus II or MATH157 Calculus & Analytic Geometry II; completion of, or concurrent enrollment in, MATH-158 Calculus III is highly recommended.
TEXTBOOK: Introduction to Mathematical Statistics & Its Applications, 5th Ed. by Marx (adopted Fall 2011) Previous: Introduction to Mathematical Statistics & Its Applications, 4th Ed., by Marx (adopted F07; 3rd Ed. adopted F01) Probability & Statistical Inference, 5th Ed., by Hogg & Tanis (adopted F01) Mathematical Statistics & Data Analysis, 2nd Ed., by Rice (adopted F97) Introduction to Mathematic Statistics, 2nd Ed., by Larsen (adopted F95) 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
4.
E. Order Statistics F. Expected Values, Variance, and Higher Order Moments G. Moment Generating Functions H. Chebyshev's Inequality 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
Updated 8/2016 Revised 7/1991 Revised 10/1971 1967
