IOE 265 Probability and Statistics for Engineers - Winter 2004 Section 200

Instructor: Luis Garcia Guzman e-mail: lgguzman-ioe265@umich.edu Lecture: Tu., Th. 1:30 PM - 3:00 PM Lecture Room: 1610 IOE IOE Office: 1777 IOE (only during office hrs) Office Hours: Tu. 12:00-1:30 (before lecture) Main Office: 407 UMTRI Phone: 734-764-5262 (Voice Mail at UMTRI Office) Note: Available at UMTRI Office only by appointment (UMTRI location: Huron Parkway/ Baxter) Graduate Student Instructors : Omer Tsimhoni e-mail: omert-ioe265@umich.edu Office: 2717 IOE Office Hours: Mondays 1:30PM-3:30PM Lab Sessions: G610 IOE Thursdays 3:30 PM - 6:30 PM Andrew Sanusi e-mail: asanusi-ioe265@ umich.edu Office: 2860 IOE Office Hours: Wednesdays 12:00 PM – 2:00 PM Lab Sessions: G610 IOE Wednesdays 2:30 PM - 5:30 PM

Course Objectives

1. Build on mathematics knowledge to understand concepts of variability and graphical representations of data

2. Know how to apply basic statistical procedures to solve engineering problems 3. Build a base of skills in drawing conclusions from data using modern statistical software

Course Outcomes

1. Appreciate the concept of variability and the importance of handling variation 2. Understand basic principles of data collection (random sampling, randomization, and blocking) 3. Know graphical and numerical techniques for summarizing and presenting data 4. Basic methods for drawing valid conclusions (inference) for different situations (confidence intervals, tests

of hypothesis) 5. Introduction to statistical software for data analysis

Date Topic Background

Reading Assignment

Due Jan 6 Course Introduction

Jan 7/8 LAB – Introduction to Minitab Jan 8 Populations, Samples, Pictorial Methods Ch. 1.1-1.2

Jan 13 Descriptive Statistics Ch. 1.3-1.4

Jan 14/15 LAB – Descriptive Statistics – Stratification Jan 15 Properties of Probability Ch. 2.1-2.2 HW1

Jan 20 Probability Counting, Permutations, Combinations Ch. 2.3-2.4

Jan 21/22 LAB – Probability Lab 1

Jan 22 Conditional Probability and Independence Ch. 2.4-2.5 HW2

Jan 27 Discrete Random Variables Ch. 3.1-3.3 Jan 28/29 LAB – Discrete Variables

Jan 29 Distributions: Binomial Distribution, Hypergeometric, Geometric, Negative Binomial

Ch. 3.4-3.5 HW 3

Feb 3 Distributions: Poisson Processes Ch. 3.6

Feb 4/5 LAB – Homework / Exam Review Lab 2 Feb 5 EXAM I (In Class~ Devore: Chapters 1-3)

Feb 10 Continuous Random Variables Ch. 4.1-4.2

Feb 11/12 LAB – Distribution Analysis Feb 12 Continuous Distributions ~ Normal Ch. 4.3

Feb 17 Continuous Distributions ~ Gamma, Exponential Ch. 4.4

Feb 18/19 LAB – Distribution Analysis (Normal, Gamma/Weibull) Lab 3 Feb 19 Continuous Distributions ~ Weibull, Beta, Probability

Plots Ch. 4.5-4.6 HW 4

Feb 23 Winter Recess – NO CLASS Feb 24 Winter Recess – NO CLASS Feb 26 Winter Recess – NO CLASS

Mar 2 Jointly Distributed Distributions Ch. 5.1-5.2

Mar 3/4 LAB – Random Number Generator / Parametric Distribution ID / Sampling Variability

Mar 4 Statistics and their Distributions Ch. 5.3 HW 5

Mar 9 Distribution of the Sample Mean/ CLT Ch. 5.4 Mar 10/11 LAB - Central Limit Theorem Lab 4

Mar 11 Distribution of a Linear Combination Ch. 5.5 HW 6

Mar 16 Point Estimation Concepts Ch. 6.1-6.2 Mar 17/18 LAB – Point Estimation

Mar 18 EXAM II (In Class~ Devore: Chapters 1-6)

Mar 23 Confidence Intervals Properties Ch. 7.1-7.2 Mar 24/25 LAB – Confidence - Sample Size Effects Lab 5

Mar 25 Confidence Intervals- Mean and Variance Ch. 7.3-7.4 HW 7

Mar 30 Hypothesis Testing – Test Procedures Ch. 8.1,8.4 Mar 31/1 LAB – Hypothesis Testing

Apr 1 Hypothesis Testing – Single Sample Ch. 8.2-8.3 HW 8

Apr 6 Hypothesis Testing - Two Samples Ch. 9.1-9.3 Apr 7/8 LAB – Hypothesis Testing Apr 8 Hypothesis Testing – Two Samples Ch. 9.4 HW 9

Apr 13 Hypothesis Testing – Two Samples Ch. 9.5

Apr 14/15 Apr 15

LAB – Hypothesis Testing Hypothesis Testing – Summary

HW 10

Apr 20 Course Summary Apr 26 FINAL EXAM (Mon, Apr 26 4:00PM - 6:00PM) Final Exam

Course Web Page: https://coursetools.ummu.umich.edu/2004/winter/ioe/265/200.nsf Lecture Notes:

All lecture notes and homework solutions will be available through the course web page. Many of the documents require Adobe reader. Lecture material will be taken primarily from the course textbook. However, the lectures provide an effective summary of the key concepts emphasized for homework and exams. Review the handouts and take your own notes during lecture!!

Textbooks:

Devore, J.L. (2004). Probability and Statistics for Engineering and the Sciences. Brooks/Cole-Thomson Learning. ISBN: 0-534-39933-9 (SIXTH EDITION) Doane, Mathieson, and Tracy. Visual Statistics 2.0. McGraw-Hill Irwin. ISBN: 0-07-240094-3 (Student Workbook and CD) – Includes required software for lab.

Recommended Text: Probability and Statistics for Engineering and the Sciences-Student Solutions Manual. Thomson Learning. ISBN: 0-534-39934-7 (SIXTH EDITION)

Other software: Minitab: available in most CAEN labs, if you would like to get your own copy, visit http://www.minitab.com

for information regarding the academic version and per term leasing on your own computer. Course Prerequisites:

Math 116 and Engin 101

Course Grading Assignment Points % of Grade

Homework (10) 90 18% Exam I 100 20% Exam II (Cumulative) 100 20% Final Exam (Cumulative) 125 25% Lab Assignments (5) 60 12% Lab – Participation 25 5%

Total 500 100%

Grading: Final grades will likely be based on a straight scale. (> 97 A+, 93-96 A, 90-92 A-, B+ 87-89, B 83-86, B- 80-82, C+ 77-79, C 73-76, C- 70-72 D+ 67-69, D 63-66, D- 60-62, F < 60). Grades may be adjusted down depending on class performance. These adjustments will occur after each exam if instructors believe an adjustment is necessary. Note: IOE Department requires a minimum of a C- in this course to graduate with IOE Degree. Exams :

• For both midterm exams, students are allowed one 8.5 x 11” formula sheet (front side only). For the Final Exam, students are allowed an additional side of an 8.5 x 11” formula sheet. Scientific calculators are allowed, but you will still be required to show calculations. If no intermediate steps are shown you will not get full credit for your answer even if it is correct.

• Majority of weight for all exam problems is for the correct approach, not necessarily the correct numerical answer. Thus, students should remember to show all relevant work. If you fail to show work, you may lose points even if you obtain a correct numerical solution.

• Make-up/alternate date exam: No make-up exams will be given unless you provide a valid excuse (e.g. medical certificate or equivalent). If you miss an exam, your score for that exam will be 0.

• Requests for re-grading of exams will only be accepted up to one week after the exam is returned to the students.

Lecture Attendance Policy: Students are expected to attend all lectures and computer laboratories. If your instructors notice that you are missing a large number of lectures, we will give you a warning for poor attendance. If you continue to regularly miss class after a warning, we reserve the right to reduce your total score by 50 points. Homework: Students are expected to complete all 10 homework assignments worth 10 points each.

• Homework assignments will be posted on the web site one week prior to their due date. • Homework assignments will be due at the beginning of lecture on Thursdays. No late submissions will be

accepted. • Homework assignment solutions will be posted on the web site. Graded homework assignments will be

returned during lab. • Requests for re-grading of homework assignments will only be accepted up to one week after the

assignment is returned. • If you complete all homework assignments (defined as answering at least ½ assigned questions), I will drop

your lowest grade. Lab Assignments: Students are expected to complete all five computer-laboratory assignments. Each lab assignment is worth 12 points. Lab assignments should be completed during computer lab hours, however, students falling behind may require additional time outside class. Lab Participation:

• Regularly attending lab and working on your lab assignments is VERY important to your instructors. Students that regularly attend Lab (defined as missing at most 1 lab sessions) AND work on their assignments during Lab will receive 25 points. Students that miss 2-3 lab sections AND/OR moderately work on their assignments during Lab will receive 15 points. Otherwise 0.

• This class is full, so students should attend their regularly scheduled computer laboratory section. If you miss your regular lab and attend another lab, make sure that all students in that laboratory section have access to a computer before taking one.

Homework and Lab Assignments

Homework # Chapter Topic Problems 1 Ch 1 Descriptive Statistics Check website

2 Ch 2 Basic Probability Check website

3 Ch 3 Discrete Distributions Check website

4 Ch 4 Continuous Distributions Check website

5 Ch 5 Jointly Distributed Distributions Check website

6 Ch 5 Statistics & Their Distributions/CLT Check website

7 Ch 6/7

Point Estimation Methods Confidence Intervals

Check website

8 Ch 8 Confidence Intervals Hypothesis Testing – One Sample

Check website

9 Ch 8/9 Hypothesis Testing – One Sample Hypothesis Testing – Two Sample

Check website

10 Ch 9 Hypothesis Testing – Two Sample Check website

Lab # Topic

1 Descriptive Statistics / Graphical Techniques

2 Basic Probability / Discrete Distributions

3 Data Analysis Summary

4 Sampling Variability of Statistic / Central Limit Theorem

5 Confidence Intervals

Honor Code: • All students are expected to be familiar with the Engineering Honor Code and are bound by its

requirements on all homework, lab exercises, and exams. Working in Teams:

• Students are allowed and encouraged to collaborate in homework and laboratory assignments. Past experience suggests that discussing problems and the approach to a solution are valuable both for the student receiving and giving information. In fact, we often learn material best by teaching others. Still, students are required to turn in their own individual work and follow all honor code guidelines related to working in teams.

Bonus Homework Assignment (10 Points):

• Provided you complete all homework and lab assignments and regularly attend lab and lectures, students may obtain 10 bonus points by completing a short one-page summary or paper describing the application of statistics or probability theory to solve a real world problem. Summaries must include a description of the problem or case study and how the problem was solved. You can use examples from manufacturing, business, service industries, health care, etc.