# MAT 321 Probability and Statistics

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### Course Description

A calculus-based survey of topics in probability and statistics emphasizing applications.

3 units credit.

### Prerequisites

MAT 193 and MAT 271 with grade C or better.

### Text

Texts are chosen by the instructor. For example:

An Introduction to Mathematical Statistics and its Applications, by R.J. Larsen and M.L. Marx. Prentice-Hall, 2nd edition, 1986.

### Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

The following is an example of an outline for this course.

• Week 1
• Arithmetic of events, distributive laws, deMorgan's laws
• Probability
• Week 2
• Conditional probability, independent events, Bayes' theorem
• Sequences and subsets, permutations and combinations, Pascal's triangle
• Week 3
• Discrete distributions: Bernoulli, binomial, geometric, hypergeometric
• Poisson distribution, Poisson's limit theorem
• Week 4
• Continuous random variables; exponential, gamma, uniform distributions
• FIRST EXAM
• Week 5
• Joint distribution functions, independent random variables
• The normal (Gaussian) distribution
• Week 6
• Transformations of random variables, random numbers
• Sums of independent random variables, convolutions
• Week 7
• Conditional densities
• Expected values, moments, covariance, variance
• Week 8
• Chebyshev's inequality, the "law of averages"
• Moment-generating functions, the central limit theorem
• Week 9
• Maximum-likelihood estimation of parameters
• SECOND EXAM
• Week 10
• Unbiased estimators, efficiency, Cramer-Rao lower bound
• Consistent estimators, confidence intervals for means, required sample size
• Week 11
• Confidence intervals for proportions, required sample size
• The statistical decision-making process, Type I and Type II errors
• Week 12
• The classical sampling distributions
• Large- and small-sample hypothesis tests of means, one- and two-sample tests, paired-sample t test
• Week 13
• The multinomial distribution, chi-square test of independence
• THIRD EXAM
• Week 14
• Covariance, correlation, linearity
• Linear regression, the least-squares principle
• Week 15
• Testing for linearity, confidence intervals for regression predictions
• REVIEW

The final exam is given at the date and time announced in the Schedule of Classes.

### Learning Objectives

After completing MAT 321 the student will

• explain the relationship between a question that arises in the natural, computer, economic, and social sciences and the nature of the numerical data that are needed in order to provide an answer to the question
• formulate the question in a mathematical context, set up the required mathematical procedure and carry out the required mathematical analysis and calculations, with appropriate use of a calculator, to answer the questions.
• choose appropriate statistical procedures for analyzing problems, explain why some statistical procedures are better than others in certain contexts.

### Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

### Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

### Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

### Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Prepared by S. Book 1/19/00. Revised 1/2/01, 7/7/01, 7/25/06 (G. Jennings)