MATHEMATICS 353
Mathematical Probability and Statistics

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

Old Lecture Notes

Reading #1 - Monty Hall, MAA Online, July 2003
Reading #2 - Baseball/Moneyball, MAA Online, September 2004

 Textbook | Course Description | Course Meetings | Grading

MAT 353 Textbook: Essentials of Mathematical Probability and Statistics, John Travis (online, opensource text)

Web Resources:

• MC Library - JSTOR Online Journals (on-campus access only)
• SAGE - online symbolic and computational software (R, Python, Octave/Matlab clone)

Prerequisites:  MAT 122.  Students who have completed MAT 121 and are currently enrolled in MAT 122 will need instructor's consent.

Writing Projects:

Useful Periodicals:

• The American Mathematical Monthly, published by the Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036-1385
• The College Mathematics Journal, published by the Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036-1385
• Mathematics Magazine, published by the Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036-1385

Sample Articles

A New Look at the Probabilities in Bingo, Agard and Shackleford, CMJ, Vol 33, #4, Sept 2002

The Average Speed on the Highway, Clevenson, et.al., CMJ, Vol 32, #3, May 2001

Perfecting the Analog of a Deck of Cards..., J.G. Simmonds, CMJ, Vol 33, #1, Jan 2002

A Rational Solution to Cootie, Benjamin and Lluet, CMJ, Vol 31, #2, March 2000

Each of these papers should be read and a written review prepared.  In the review, the student should point out the major points of the article including how the article related to the material being studied in this class.  Comments on the examples presents and on "obvious" statements given should be included.  Any extensions, applications or connections to other material that the student discovers should be included..

Course Outline: 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 semi rigorous mathematical viewpoint using concepts developed in Calculus. We will use this framework to carefully discuss making such statistical inferences as above and in general to obtain accurate knowledge even when the known data is not complete.  For general mathematics majors, this course satisfies the applied area requirement (III) listed in the college catalog.  For math education majors, this course is required.

This course carries three hours of academic credit.  

(From the college catalog: This course is a calculus based introduction to probability and statistics.  Major emphasis is placed on developing a precise framework for solving problems under uncertainty.  Topics covered include expected value, probability density functions and their distributions, interpretation of the Central Limit Theorem and its application to confidence intervals and hypothesis testing.)

Learning Objectives:  This term, we will rigorously investigate the following concepts:

• various descriptive measures and methods including:
  • random variables
  • measures of the middle and the spread
  • how to deal with grouped data
• expected value and distribution measures
• discrete random variables, their distribution properties and how to apply them
  • uniform
  • hypergeometric
  • bernoulli
  • binomial
  • geometric
  • negative binomial
  • Poisson
• continuous random variables, their distribution properties and how to apply them
  • uniform
  • exponential
  • normal
  • others, as time permits
• grouped data and the Central Limit Theorem
• confidence intervals
• statistical tolerance intervals
• various types of hypothesis testing (as time permits)

Specific NCATE objectives satisfied:

• Use appropriate methods such as random sampling or random assignment of treatments to estimate population characteristics, test conjectured relationships among variables, and analyze data.
  • Informal experiments will be performed during class using data collected from the participants. Some assignments--in particular one dealing with the "birthday problem"--will be used to test a specific conjecture derived in class. Further, various software resources will be utilized to simiulate random sampling on a large scale.
  • Comparisions between generated sample statistics and theoretical population parameters will be explored and noted. Special attention will be focused on the law of large numbers and on the tendency toward distributions to become increasingly bell-shaped as parameters are changed.
• Use appropriate statistical methods and technological tools to describe shape and analyze spread and center.
  • Classroom presentations will focus on the development of formulas for center and spread for the Binonial, Geometric, Negative Binonial, Hypergeometric, Poisson, Uniform Continuous, Exponential, Gamma and Normal Distributions.
  • Numerous Sage worksheets will investigate numerically and symbolically the mean, variance, skewness and kurtosis for each of these and provide the ability to experiment dynamically with parameters and to judge the effect as they are changed.
  • The online homework system WeBWorK will be utilized to test student's understand of basic ideas and computational formulas. This will include determining sample means and variances.
• Use statistical inference to draw conclusions from data.
  • Various statistical measures will be developed and utilized to make judgements regarding data.
  • Confidence intervals will also be derived for means and proportions.
• Identify misuses of statistics and invalid conclusions from probability
  • Special attention is paid to the derivation of methods from basic principles.
  • Focus will be made on when distributions apply and when they do not.
• Draw conclusions involving uncertainty by using hands-on and computer-based simulation for estimating probabilities and gathering data to make inferences and conclusions.
  • Experiments will be performed using various software resources to simulate numerous models using Winplot and Sage. One special simulation will be used to demonstrate how increasingly larger sets of random sample means generate a bell-shaped distribution

Meetings: The format of class meetings will consist generally 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 (See the Undergraduate 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.  (For the University Policy on disabilities, check the MC website).

Grading: There will be at least three sectional exams during the semester (with no comprehensive final). Makeup exams will be administered at the instructor's discretion only in case of a valid excuse given prior to the exam period. Also, selected homework/projects--often within the SAGE computing environment--will be graded.  Your final average will be computed by considering the homework/project average as an exam grade and then taking the average of this with all of the exams. The grading scale is

A=90-100
B=80-89
C=70-79
D=65-69
F=0-64

Aim now for the desired grade.  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.