# IE 111: Engineering Probability and Statistics

## Syllabus: Fall Semester 2011

### Course Description

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
Upon completion of this course, students will:

·        Know the basic axioms and set theory upon which probability theory is based including sample spaces and events, mutual exclusivity, conditional probability, independence, and Bayes theorem.

·        Be able to solve problems in counting and probability using techniques including permutations, combinations, permutation of like objects, “multi-choose”, and probability trees.

·        Understand the concept of random variables and probability mass functions, densities, and distributions.

·        Understand the concept of expectation and be able to apply it in decision making

·        Understand the mean and variance of a random variable.

·        Understand Chebyshev's  inequality.

·        Know various well-known distributions and how they are used in practice.

·        Understand Poisson processes and what they are used for in practice

·        Understand joint, marginal, and conditional distributions

·        Understand covariance and correlation

·        Be able to apply probability theory to solve probability problems.

·        Be able to apply the theory of expectation to solve decision problems involving the maximization of expected return

### Prerequisites

Math 22 (Calculus II) is a pre-requisite. You should be taking Math 23 (Calculus III) this semester, or have taken it already, since we will use some material from it (double integrals, in particular) later in our course. If you have not taken Math 22, or are retaking it this semester due to grades, you should drop this course now; we will offer it again next semester. In past years we sometimes let students who didn't have the prerequisite into IE 111, only to see them struggle all semester long and end with very unsatisfactory grades.

### Contact Information

`Professor`
`Dr. Robert H. Storer `
`477 Mohler Lab, 758-4436`
`E-mail rhs2@lehigh.edu`
`Home Page: www.lehigh.edu/~rhs2/rhs2.html`
`Office Hours: MF 10-11:30 and .W 2-3`
` `
`Teaching Assistant`
`Mr. Hao Wang`
`350 Mohler Lab`
`Office hours: Tuesday: 8:40am-10:40am Thursday: 1:00pm-3:00pm`
`758-6703`
`haw309@lehigh.edu`

### Textbook (required)

"Applied Statistics and Probability for Engineers": Fifth Edition, Douglas C. Montgomery and George C. Runger, published by John Wiley and Sons and the associated "Student Workbook with Solutions", by Heecheon You.

We will be covering the following chapters in the following order: 2, 3, 4, 5. There will be 4 midterm (50-minute) exams, at (approximately) the ends of chapters 2, 3, and 4 (see schedule). The final will be cumulative, but with extra emphasis on chapter 5.  Also, you will almost surely use the same textbook when you take IE 121 next semester, so do not sell it back to the bookstore at the end of this semester.

### Web Page

We will post some things, including homework assignments, the tentative course schedule, and this syllabus, on the course web page using Coursesite. To reach it, go to

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### Course Philosophy

I see this course as a partnership between the textbook, lectures, and homework; all of them work to help you learn. Tests serve to ensure that you are learning the material, but they cannot test everything all at once. There will be problems on the homework that are much harder than anything that would be on a test. The homework is supposed to be hard, just like training for a sport. You should allocate enough time for it; ideally, you should start it well before office hours, so you can use office hours efficiently. Because no textbook is perfect, there will occasionally be items presented in lecture that are not in the book. You will be responsible for these topics just as much as the ones that are in the book. Similarly, there are some things in the textbook that are better read than lectured. Just because it didn't appear in lecture doesn't mean it won't be in the homework or on the exams.

Integrity and Honesty are vital in life, especially for engineers, since the systems we design or modify can improve people's quality of life, or can do irreparable harm. Using probability and statistics ethically requires that we state all of the facts and assumptions in as clear a manner as possible, to avoid "lying with statistics". We are also bound by honor to give credit where it is due. In this class, you might ask others for help with a homework assignment. Once you write up your answer in your own words to turn in, it is a good idea to include a mention of their help on any particular problem. It is dishonest to copy homework solutions from past years that you might obtain or have. On quizzes and exams, of course, your work should be entirely your own. Violations of academic honesty will result in disciplinary proceedings.

Here is the statement of the Lehigh Student Senate on academic integrity: We, the Lehigh University Student Senate, as the standing representative body of all undergraduates, reaffirm the duty and obligation of students to meet and uphold the highest principles and values of personal, moral and ethical conduct. As partners in our educational community, both students and faculty share the responsibility for promoting and helping ensure an environment of academic integrity. As such, each student is expected to complete all academic course work in accordance to the standards set forth by the faculty and in compliance with the University's Code of Conduct.

Your final numeric score will be determined as follows:

`  `
`22% : Homework (11 assignments)`
`  5% : Class participation        `
`48% : Midterm exams (4 of them, 12% each)`
`25% : Final Exam`

### Accommodations for Students with Disabilities

If you have a disability for which you are or may be requesting accommodations, please contact both your instructor and the Office of Academic Support Services, University Center 212 (610-758-4152) as early as possible in the semester. You must have documentation from the Academic Support Services office before accommodations can be granted.

Aside from verified disability accommodations, no exemptions from exams will be given, and no exam scores will be dropped. Only verifiable excuses will be considered for missing an exam: you must inform me prior to the exam, and you must supply me with a written excuse from a doctor or the Dean of Students.

### Typical Difficulties

Here, we list some of the problems that students typically encounter in the course. You won't understand some of the terms right now, but look back at this section as the course goes along and you will understand it better.

The hardest part of this course is usually figuring out which type of probability distribution to use in a particular situation. That is, "word problems" are what this course is all about. This is not made easier by the fact that the names of the distributions, like the names of the chemical elements, have no apparent system to them. It takes a lot of practice to become familiar with what tool to use for any particular situation, so hang in there, practice, and it will eventually "click" for you.

Other difficulties tend to be:

• Accidentally reporting the probability of something NOT happening, instead of it happening, or vice versa.
• Getting mixed up between "all parts are not bad" and "not all parts are bad".
• Figuring out when an approximation is justifiable.
• Remembering the difference between "independent" and "mutually exclusive".
• When to use Var(X1+X2+X3) and when to use Var(3*X1)

### Schedule Notes

Do not purchase your Winter break airline tickets before the schedule for final exams is posted. You will not be allowed to "take the exam early because you have already purchased a non-refundable airline ticket". The last possible day for the exam is Wednesday, Dec. 22nd.