MATHEMATICS 453/5462

Mathematical Statistics

John Travis
MCC 206
925-3817 (voice mail)
travis@mc.edu (email)

Notes | Math 253 Notes


Textbook: Probability and Statistical Inference, 7th edition, Hogg and Tanis

Prerequisites:  MAT 353 or Graduate standing with instructor's consent.

Course Description: People often make claims about being the biggest, best, most often recommended, etc. One sometimes even believes these claims. In this class, we will attempt to determine if such claims are reasonable by first introducing probability from a rigorous mathematical viewpoint using concepts developed in Calculus. We will use this framework to carefully discuss making statistical inferences to obtain accurate knowledge even when the known data is not complete. The prerequisite for this class in Math 353. Some of the material from 353 will be repeated but at an accelerated and more in-depth manner. Further, multi-dimensional statistics will be developed and more attention will be paid to statistical applications.
This course carries three hours of academic credit.
 (From the college catalog:  This course develops rigorous proofs for the results presented in MAT 353  Multivariate Statistics is also covered.  Linear regression and the analysis of variance will be discussed as well as applications of the theory.)
Learning Objectives: This term, we will investigate the following concepts:
  • Review and discuss generating functions for the following discrete distributions
    • hypergeometric
    • bernoulli
    • binomial
    • geometric
    • negative binomial
    • Poisson
  • Review and discuss generating functions for the following continuous distributions
    • exponential
    • normal
  • Develop the Gamma Distribution and Chi-Square Distribution
  • Functions on random variables
  • Grouped data and the Central Limit Theorem
  • Applications of the Central Limit Theorem
  • Creating and using confidence intervals
  • Creating and using statistical tolerance intervals
  • Hypothesis testing
  • Multi-variate statistics

    • Meetings: The format of class meetings will consist of lectures by the instructor. Student participation will be encouraged via classroom discussions as well as problem sessions where the student will present their work.  This class meets as scheduled. You are expected to be in class on time.  University policy states that a student cannot miss more than 25% of class meetings and receive credit for the course. Further, attendance will be necessary in order to understand the material and make a good grade. The student is responsible for work and material missed when absent. Cheating in any way will be properly rewarded according to University policy (Tomahawk; Undergrad. Bulletin)

    If you need special accommodations due to learning, physical, psychological, or other disabilities, please contact the Counseling and Career Development Center by phone at (601)925-3354 or by mail at P.O. Box 4013, Clinton, MS 39058.

    Grading:
    "Graduate students should read the Graduate Orientation Manual in its entirety.  This is an important part of the orientation for graduate students.  Please get your hard copy from your department or from the Graduate Office in Nelson 202.  You may also view the manual on the web at this address:  http://www.mc.edu/publications/graduate/orientation.html"

    Aim now for the desired grade. Finally, all graded work will be returned to the student for keeping. If there were any question later about your grade, you would be expected to show these papers.