Math 301                       Mathematical Probability and Statistics
Spring, 2004                   Westminster College
C. K. Cuff, Ph.D.            Office hours M, W,  F  10:30-11:30 and by appointment
Hoyt 154                                               T Th by appointment
x7291                                                   

 

Description of the course:  An introduction to the mathematics of basic probability theory and the mathematics of statistical inference.  Topics include discrete and continuous random variables, bivariate and multivariate distributions, point estimators, and measures of their quality.

Prerequisite: Successful completion of Math 141, Math 211, Math 251, and a computer science programming course.

Text:  Wackerly, Mendenhall, and Scheaffer, Mathematical Statistics with Applications, 6th edition, Duxbury Press, 2002.

Goals:

  • Learn the concept of probability within the context of a mathematical system with axioms, definitions, and theorems.
  • Apply appropriate probability distributions to model uncertain events.
  • Learn some of the mathematical underpinnings in the selection of estimators.

 

Objectives:

  • Solve all probability problems at the Math 211 level.
  • Demonstrate understanding via problem-solving, explanations of proofs, and oral presentations of binomial, geometric, negative binomial, hypergeometric, Poisson, gamma, and beta probability distributions and the appropriate connections between these distributions.
  • Explain and apply Tchebysheff’s Theorem within appropriate contexts.
  • Demonstrate understanding of conditional probability distributions, marginal probability distributions, expected value of function of random variables, independence and covariance of random variables both within an applied and theoretical setting.
  • Explain the mathematical properties of a good estimator.


Expectations:

  • You are expected to prepare for each class.  Preparation includes: reading the assigned sections and completing the assigned problems and exercises.
  • You are expected to attend each class and be an active participant in the class.
  • You are expected to meet outside of class with your classmates to discuss the homework questions.
  • You are expected to have and use the reference guides of the previous courses. You are responsible for the materials which have been covered in the listed prerequisite courses.  I do not plan a formal review of this material.

 

Assessment:

 

Material graded in this course will include:

  • homework problems and exercises                                       15%
  • an oral presentation of a probability application paper            10%
  • a statistics project                                                                 10%
  • two examinations                                                          each 15%
  • comprehensive final                                                               35%


 

Final grade calculation

 

90-100    A      78-78.99 C+

89-89.99 A-     70-77.99 C
88-88.99 B+     69-69.99 C-
80-87.99 B       60-68.99 D
79-79.99 B-     0-59.99    F

Tips for success in college math (suggested reading - even if you've been successful)

Tentative topic outline

Probability

Conditional probability
Bayes’ Theorem


Expected Values, Variance and functions of expected values and variances
Tchebysheff’s Theorem and its use

 

Discrete Random Variables, when to, how to use, (includes means, variances)

General

Geometric

Negative Binomial

Hypergeometric

Poisson

Moment generating functions

 

Continuous Random Variables, when to, how to use, (includes means, variances)

General

Uniform

Normal

Gamma

Beta

 

Joint Distributions

General

Marginal

Conditional and Independent

Expected Value

Covariance

 

Multinomial Distributions

Order Statistics

 

Statistics

Unbiased Estimator
Given a choice between two estimators - choose the best one based on minimum variance.

 

Analysis of Categorical Data

Chi-Square Test

Goodness of Fit test