Math 330—Probability and Statistics
Syllabus—Spring 2008

Catalog Description

A calculus-based examination of probability, discrete and continuous random variables, sampling theory, confidence intervals, and hypothesis testing. Spring odd years.
Prerequisites: MA 200, MA 240, MA 250.

Rationale

Probability theory and statistics are a significant area of mathematical inquiry and are widely applied in other disciplines. They are powerful tools for modeling and decision making in business and industry, and in the physical, life, and social sciences. This course provides a study of probability, the mathematical basis of statistical applications, and testing, and some applications of probability and statistics. The course encourages students to draw upon knowledge gained in other courses. It is a significant course in the professional background of the mathematics graduate, students studying in actuarial sciences, economics and related fields, or physical and life sciences.

Goals

1. Apply the concepts of probability.
2. Use counting principles to compute probabilities.
3. Compute conditional probabilities, including the use of Bayes’ Rule and determining the independence of events.
4. Determine probabilities, moments, and moment generating functions for discrete and continuous probability distributions.
5. Use probability models including binomial, Poisson, and normal in applications.
6. Apply probability distributions to elementary statistical inference.

Competencies

At the conclusion of this course, the student will be able to:

1. Compute probabilities using the axioms of probability and counting principles.(Math SSC 4.2, 7.1)
2. Determine probabilities of events using probability distributions and their properties. (Math SSC 4.2, 7.1)
3. Apply axioms of probability, counting principles and distribution functions in the solution of applied problems. (Math SSC 4.2, 7.1)
4. Calculate expected values, moment generating functions, and moments. (Math SSC 7.2)
5. Use a variety of methods to determine the distribution of a sample statistic. (Math SSC 7.1, 7.2)
6. Apply sampling distributions to elementary inference procedures. (Math SSC 4.2, 4.3)
7. Derive distributions of random variables. (Math SSC 7.2)
8. Understand the role of descriptive statistics in data analysis. (Math SSC 4.1, 7.3, 7.4)
9. Utilize the chi-square, t, and F distributions and understand their significance. (Math SSC 7.2, 7.4)
10. Work with confidence intervals and understand their parameters. (Math SSC 4.2, 7.3)
11. Perform hypothesis tests and discern among the standard types of errors. (Math SSC 4.3, 7.3, 7.4)
12. Perform regression analyses. (Math SSC 7.1, 7.2, 7.3, 7.4)

Performance indicators:

These competencies shall be assessed primarily by means of written work and written examinations. Additional assessment may take place by means of observation of in-class activities and discussion.

Course Information

Required Textbook

Miller, I. & Miller, M. (2004). John E. Freund’s Mathematical Statistics with Applications, (7^th ed.), Upper Saddle River, NJ: Prentice Hall.

Bibliography

Moore, D. S. & McCabe, G. P. (2003). Introduction to the Practice of Statistics, (4^th ed.), New York: W. H. Freeman and Company.

Miller, I. & Miller, M. (1999). John E. Freund’s Mathematical Statistics, (6^th ed.), Upper Saddle River, NJ: Prentice Hall.

Thomas, G. B. & Finney, R. L. & Weir, M. D. & Giordano, F. R. (2001). Thomas’ Calculus, (10^th ed.), Boston: Addison Wesley.

Calculators and Computers

A graphing calculator is recommended but not required. Graphing devices vary greatly so you should use your manual and become familiar with your own calculator and its features. Most statistical calculations and graphics can be produced through software and is done so in practice. We may use the statistical capabilities of Microsoft Excel at various times during the semester.

Course Requirements and Evaluation

Final grades will be determined by the percentage of possible points earned from Portfolio, Quizzes, Exams and Final according to the following scale:

The instructor reserves the right to make modifications to this grading policy as needed.

Portfolio

The portfolio will include assigned homework and various short writing assignments. You will be asked to turn in your portfolio for review at midterm and at the end of the semester. Homework will be assigned on a regular basis. I recommend that you come to my office to see me about any homework problems that are causing you difficulty.

Quizzes

There will be a quiz over each section or two covered. Questions on each quiz will be based on the homework assignments. Each quiz is worth 30 points. You cannot make up a missed quiz. At the end of the semester, each student’s two lowest quiz scores will be dropped.

Reading

I expect you to read the text prior to our class meetings. This will help prepare you for the class presentation and class discussion.

Exams

The exact dates for exams will be announced in class. Make-up exams are only allowed for validated illnesses, emergencies, and college-related activities such as field trips or sporting events, where your name is on the list of excused students. It is your responsibility to contact me before the exam if you know you will miss the exam and arrange with me to take the make-up exam before the next class session. A longer delay in taking the make-up exam will result in up to a 30% discount in your grade. Failure to contact me before a missed exam will result in a zero for the exam. Also, if you miss an exam and do not take the exam before the tests are handed back in class you will receive a zero for the exam. Extenuating circumstances will be treated on a case-by-case basis.

Attendance

Attendance is expected. Attendance will be taken at the beginning of each class period. Please inform me in advance of any planned absences. For illness or emergencies, contact me to arrange to make up any missed work.

If you miss more than 50% of a class at any given point in the semester, you will be dropped from the class. This will be recorded as a withdraw/fail. Any student who misses two consecutive weeks of class will be administratively withdrawn from class. If the withdrawal takes place within the first 6 weeks of class, the student will receive a grade of “W”. If the withdraw takes place after the 6^th week of class, the student will receive a “WF” or “WP”. The student will be notified of the action by the Registrar’s Office. Readmission will be considered only for extenuating circumstances as approved by the Vice President of Academic Affairs and Registrar. In such cases, where readmission is approved, a readmit fee of $350 will be charged. If a student drops below full-time status of 12 hours, financial aid may be adversely affected. Resident students dropping below 12 hours will be asked to move out of campus housing.

Note: If you know that you want to drop or withdraw from a class, please see your advisor. Do not count on this policy to automatically withdraw you.

Tentative Schedule

Final Exam: 10 a.m., Thursday, May 1

You must take the final exam at the time designated for your class. The final exam is mandatory. Make your travel arrangements accordingly.