STAT 407 Introductory Mathematical Statistics (3)

 Catalog Description:

Mathematical theory underlying probability, statistical estimation, and hypothesis testing: random variables and their distributions, distributions of functions of random variables, sampling distributions, limiting distributions, and the Central Limit Theorem. (Offered fall semester, odd years.)

 Prerequisites:

MATH 211 Calculus III and STAT 291 Statistics for Mathematical Sciences I

  1. Familiarity with topics in probability: axioms and properties, counting techniques, density and distribution functions, expectation, conditional probability, independence, and correlation.
  2. Familiarity with common discrete and continuous distributions.
  3. Understanding of the Central Limit Theorem and its applications.
  4. Familiarity with techniques of mathematical proofs.
  5. Ability to differentiate and integrate functions of several variables.
 Required Course Materials:

R. Hogg, J. McKean, and A. Craig, Introduction to Mathematical Statistics, 6th edition, Prentice Hall, 2005 (ISBN 0-13-008507-3)

Prerequisite course material: J. Devore, Probability and Statistics for Engineering and the Sciences, 7th edition, Brooks/Cole, 2007 (ISBN 0-495-38217-5)

 Course Coordinator:

L. Marlin Eby, Ph.D., Professor of Mathematics and Statistics

 Course Audience:
    1. Students majoring in mathematics or minoring in statistics.
    2. This course can be used to meet the elective requirement for mathematics majors.
 Course Objectives:
    1. To use probability in applied models and as the foundation of inferential analysis.
    2. To intuitively understand each concept.
    3. To understand the rigor of a mathematical proof.
    4. To integrate topics by identifying commonalties.
    5. To understand the limitations of each analysis through consideration of assumptions.
    6. To use general concepts to solve theoretical and applied problems.

 Topics:
    1. Distributions of Random Variables: probability set, density, and distribution functions; mathematical expectation, and Chebyshev's inequality.
    2. Conditional Probability: marginal and conditional distributions, correlation, and stochastic independence.
    3. Specific Discrete Distributions: probability calculations, moments, moment-generating functions for hypergeometric, binomial, multinomial, and Poisson distributions.
    4. Specific Continuous Distributions: probability calculations, moments, moment-generating functions for uniform, univariate and bivariate normal, and gamma (including exponential and chi-squared) distributions.
    5. Distributions of Functions of Random Variables: transformations of discrete and continuous random variables, t and F distributions, order statistics, sampling distribution of the mean and variance, and expectations of functions of random variables.
    6. Limiting Distributions: definition, stochastic convergence, limiting moment-generating functions, Central Limit Theorem and other theorems.
 
Reviewed: August 2011