Syllabus for Math 3623 Mathematical Statistics

PREREQUISITES: Math 2614 - Calculus I

CATALOG DESCRIPTION OF COURSE: Descriptive statistics; probability and combinatorial methods, discrete and continuous probability distributions and densities including multivariate, marginal, and conditional distributions of random variables; sampling distributions, mathematical expectation; simple linear regression and correlation. Credit may not be earned in both MATH 3623 and 3513 in the math major. Prerequisite: Math 2614.

COURSE PURPOSE: This is a calculus-based introductory statistics course. Mathematics education majors, as well as computer science majors (math emphasis) are required to take either this course or Statistical Methods. This course is also an elective for mathematics majors. It is intended to explore the mathematical basis of statistical methods. The course is also designed to enable students to perform a variety of basic statistical analysis utilizing these methods.

EXPECTED COURSE OUTCOMES: Students will be expected to achieve the following objectives:

1. Summarize and describe data sets effectively.

2. Use basic probability concepts in problem-solving.

3. Recognize specific probability distributions and utilize them in problem-solving.

4. Determine expected values, joint distributions, marginal distributions, and

independence of random variables.

5. Utilize appropriate methods to estimate population parameters.

6. Demonstrate an understanding of the logic of hypothesis testing by performing

appropriate hypothesis tests.

7. Appropriately interpret and communicate the results of a variety of standard statistical analyses.

INSTRUCTIONAL MATERIALS: (Required Textbook) Christensen, Howard B. Introduction to Statistics: A Calculus-Based Approach. Fort Worth: Saunders College Publishing, 1992.

INSTRUCTIONAL PROCEDURES:

The expected course outcomes will be realized primarily through lecture, discussion, and demonstration.

Mathematical Statistics

I. Describing Data

A. Vocabulary

B. Graphical Methods

C. Numerical Methods

II. Probability - Part 1

A. Terminology

B. Probability Rules

C. Counting Methods including combinations and permutations

D. Conditional Probability

E. Probability Functions

F. Distribution Functions

G. Moment Generating Functions

III. Probability - Part 2

A. Joint Probability

B. Marginal Probability

C. Expectation

D. Independence

E. Discrete Probability Functions

F. Continuous Probability Functions

IV. Sampling Distributions

A. Definition

B. Central Limit Theorem

C. Related Distributions

V. Estimation

A. Method of Moments

B. Method of Maximum Likelihood

C. Interval Estimation

VI. Hypothesis Testing

A. Concepts

B. Errors

C. One Sample Test of Means

ADA COMPLIANCE:If any member of the class feels that he/she has a disability and needs special accommodations, please advise the instructor of such disability at the first class attended.

INCLEMENT WEATHER / DISASTER POLICY: The following are basic premises for the inclement weather policy at Northeastern State University:

1. Classes are expected to be held if at all possible.

2. It is the student's responsibility to receive the information when weather is questionable.

3. Neither students nor faculty are expected to risk life or limb.

4. Faculty members are obligated to hold classes if the University is not closed, unless the faculty member is unable to get to campus.

Policy: During times of inclement weather, decisions concerning day classes will be made by 6:00 a.m. in order for the media to be notified and for students to receive the announcement before they leave home. Decisions concerning night classes will be made by 3:00 p.m.

The following media will be notified regarding closing of the campus:

Radio Stations: Television Stations:

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The automated attendant message on 918-456-5511 will be modified to include information concerning campus operations during inclement weather.