Engineering Probability and Statistics

This course is an introductory course to the fields of Probability and Statistics designed for engineering students. The course focuses primarily on the study of Probability Theory. We may also cover some Statistics toward the end. Probability Theory is of great use in all branches of Engineering in understanding and modeling phenomena that exhibit random behavior. Probability Theory also provides the theoretical and mathematical basis for statistics, and thus must be studied first.

The field of Statistics pertains to the presentation, analysis and interpretation of data. Engineers will be faced with the need to analyze data on a daily basis in the real world, and thus a good grounding in the basics of statistics is invaluable. Statistics is inherently inductive since inference is made about a whole population on the basis of information/data obtained from a sample from the population.

Unlike Statistics, Probability theory is inherently deductive, and has nothing to do with sample data. Rather it is a field of mathematics from which results and conclusions are derived from propositions and assumptions. A typical easy problem that one could solve using probability theory is "given that the probability of a coin flip coming up heads is 0.5, what is the probability that I will get exactly 5 heads if I flip the coin 10 times?" Note the absence of any sample data in this problem. Given an assumption (probability of a head is 0.5) one deduces the conclusion (the probability of exactly 5 heads is 0.2461).

Statistics is probably more useful for most engineers than probability. However, the theory that underlies statistics is probability, which makes its study necessary as well. The study of Probability Theory can be fun and interesting, but also difficult, confusing and frustrating. In particular, the use of counting methods to compute probabilities, which comes early in the class, is likely the most confusing and frustrating part of the course (in addition to hopefully being fun).

COURSE OBJECTIVES: The student who successfully completes this course will have:

1. an understanding of the basic principles of exploratory data analysis.
2. an understanding of the basic principles in probability, mathematical expectation, and various probability distributions.
3. an understanding of the basic principles of statistical inference (i.e., estimation and hypothesis testing).
4. skill in applying the basic principles of statistical inference to practical problems.
5. an understanding of some of the basic ideas of reliability theory.
6. experience in the use of a statistical computing package.

Course Text:
Montgomery, Douglas C. and Runger, George C. (2011). Applied Statistics and Probability for Engineers, Fifth Edition. John Wiley and Sons, Inc.