MATH 361 PROBABILITY AND STATISTICS I (4-0-4)
Calculus-based treatment of probability theory, random variables,
distributions, conditional probability, central limit theorem, descriptive
statistics, regression and correlation, tests of hypotheses, design of
experiments, and sampling surveys. Differs from MATH 360 by providing more
thorough coverage of theoretical foundations and wider variety of
applications, which are drawn from natural and social sciences as well as
engineering. PREREQ: MATH 175.
Second semester calculus. The rationale for this prerequisite is to ensure that students have an adequate level of ``calculus maturity," in particular some familiarity with basic integration techniques.
The instructor has complete control over the teaching of this course, including the examinations, homework, and grading system.
This calculus-based introductory course in probability and statistics is designed for engineering and physical science majors as well as for mathematical science students. When successfully mastered, this course is one of the best at advancing a student's facility in applied mathematics and general problem solving. Further, a student completing the course should be able to obtain additional specific statistical tools on his/her own.
Mathematical statistics is certainly a classic application of mathematics using, among other tools, both continuous and discrete methods. It develops a rich and precise notation. Results like the central limit theorem exemplify elegant mathematics.
Upon completion of the course students should be able:
1. to solve the traditional problelms of elementary probability and statistics.
2 to recognize, formulate and interpret the results of hypothesis testing, regression and estimation.
3. to use the basic results on binomial and normal random variables and to be aware of the limitations of these results .
Students will be evaluated on their ability to do problems, both as homework and as formal examinations. The problems will be of two types:
1 to reinforce the material in the text, and
2. to extend the results and ideas to new situations
The following table is based on a typical semester schedule-60 class meetings
of 50 minutes each. The actual amount of time spent on each topic will
vary slightly from semester to semester and instructor to instructor.
| Number of | |
| Topic | Meetings |
| Enumeration and Algebra of Sets | 4 |
| Basic Definition and Properties of Probability | 4 |
| Conditional Probability and Independence | 4 |
| Distributions of Discrete Random Variables | 6 |
| Distributions of Continuous Random Variables | 5 |
| Basic Sampling Theory | 5 |
| Introduction to Estimation | 5 |
| Introduction to Hypothesis Testing | 6 |
| Regression Analysis | 5 |
| Analysis of Variance | 6 |
| Further Chi-Square Tests | 6 |
| Exams | 4 |
The latest editions of the following have been used in the recent offerings of this course:
Probability and Statistics for Engineering and the Sciences, Devore, J., Brooks/Cole Pub. Co. 1991.
Probability and Statistical Inference, Hogg, R. & Tanis, E., Macmillan Pub. Co., 1992.
Class meetings involve a combination of lecture, questions and discussion.
Homework is an important part of the course. Perhaps the large amount
of ``classical knowledge' required in this course forces it to be taught
in a traditional
lecture-homework-exam mode. The instructor chooses the exact grading
scheme, with a typical distribution being:
| Homework | 150 |
| 4 Exams | 400 |
| Final Exam | 250 |
| Total Points | 800 |