Announcements
Office Hours are:Sundays, 7-9pm, Terman 453
Mondays, 8:45-9:30am (in the classroom)
Mondays, 3-4pm, Terman 401
Tuesdays, 3-4pm, Terman 401
Wednesdays, 8:45-9:30am (in the classroom)
Wednesdays, 1-3pm, Terman 490
Thursdays, 6-8pm, Terman 479
Fridays, 8:45-9:30am (in the classroom)
Note that office hours will not be held during takehome exams.
Course Objective
This is a fast-paced, fundamental course designed to develop an understanding of uncertain phenomena using the theory of probability. The course objective is to provide students with conceptual and intuitive insights into probabilistic reasoning and the ability to solve real world problems.Intended Audience
For students seeking an introduction to probability theory and applications, this course is designed to develop their intuition and model building skills. This course is intended for undergraduate students and should be taken for five units. This course satisfies the Distributional Breadth GER in Engineering and Applied Science.(Graduate students should enroll in a similar course, MS&E 220, taught separately.)
Course Summary
Concepts and tools for the analysis of problems under uncertainty, focusing on model building and communication: the structuring, processing, and presentation of probabilistic information. Examples from legal, social, medical, engineering, and physical problems provide motivation and illustrations of modeling techniques. Spreadsheets will be used to illustrate and solve problems as a complement to analytical closed-form solutions. Topics include: axioms of probability, conditioning and probability trees, random variables and distributions, expectation, and limit theorems. Prerequisite: Mathematics 51. Recommended: some knowledge of spreadsheets.Required Textbook
The required textbook for the course is Sheldon Ross, A First Course in Probability, Prentice Hall, 2006 (Seventh Edition).Hardware/Software Requirements
Every student is expected to have access to a spreadsheet program, such as Microsoft Excel. (This access can be through clusters on campus and will come in handy for other courses in the MS&E program.)Prerequisites
Students should have a working knowledge of calculus at the level of Math 51, including some multiple variable integration.Because we will use spreadsheets to illustrate and solve some problems, it will help to understand some basic operations.
Skills you should acquire or strengthen in this course
After taking this course, you should have- an intuitive understanding of probabilistic concepts sufficient to apply them in practice;
- the ability to solve real world problems under uncertainty by
- structuring problems,
- building models,
- analyzing and processing those models, and
- communicating insights.
Opening Your Eyes
Please sensitize yourself to newspaper or magazine articles or observations about uncertainty that you encounter. You won't get course credit for doing this, but it will help to awaken you to the uncertainties that challenge us and it will enhance your course experience.Honor Code
The Honor Code is taken seriously at Stanford University and we expect it to be respectfully observed by the course staff and students. Simply put, it places the responsibility for ensuring honest behavior on the students rather than the course staff, and violations should not be tolerated. The midterm and final examinations are strictly individual work and you are not permitted to consult on them with others. You can consult with others on the homework assignments but you must acknowledge their assistance.Please contact Prof. Shachter if you have any questions about the Honor Code or the requirements for any assignment.
Grades
The course grade will be based on five bi-weekly homework assignments, two take home midterm examinations, and a final examination, with the following weights and with borderline decisions affected by class participation:
Here is the distribution of grades from last year's class:
| Grade | Percentage |
|---|---|
| A+ | 3% |
| A | 17% |
| A- | 27% |
| B+ | 19% |
| B | 14% |
| B- | 13% |
| C+ | 5% |
| C | 3% |
Examinations
There will be two take home midterm examinations, due at the start of class on Mondays, October 20 and December 1. You will have one weekend to complete the first and the second will be distributed before Thanksgiving. Late submissions will be penalized.There will be a final examination from 8:30 to 11:30am on Thursday, December 11 in a location to be determined. The exam will be open-book and open-notes. Students can request to take an alternate exam to be given Friday, December 12 from 8:30 to 11:30am in a location to be determined.
All students are responsible for ensuring that they can attend either the regular or alternate final exam and complete the take home midterm exams.
Homework
Solving these problems is the best way to learn the material and prepare for the examination and take home assignments. You should submit your completed and partial solutions to the assigned problems but your grade will be based solely on your effort. Come see us, early and often, if you have questions. Homework is due at the start of class on alternate Mondays (or before class in Terman 405). It is important to keep up and we cannot help you unless you help yourself first. We would prefer you stay current and not fall behind. Therefore, we will penalize late homework.You are welcome to work with others to master the principles and approaches used to solve homework problems, although the work you turn in should be your own. Copying the work of others would provide you no educational value and would violate the spirit of the Honor Code. In the spirit of academic integrity and the Honor Code, you must acknowledge all of the people and materials you have consulted, including course staff and handouts, in preparing your submissions.
| Assignment | Problems from the Text |
|---|---|
| Homework 1 due Sept 29 | Chapter 1
Problems 3, 7, 8, 12, 13, 14, 15, 19, 21, 22, 32, 33 Theoretical Exercises 2, 3 Chapter 2
|
| Homework 2 due Oct 13 | Chapter 2
Problems 12, 15, 21, 43, 44, 45, 52, 56 Theoretical Exercises 15 Chapter 3
Chapter 4
|
| Homework 3 due Oct 27 | Chapter 4
Problems 32, 38, 43, 48, 52, 58, 60 Theoretical Exercises 4, 9, 27 Chapter 5
|
| Homework 4 due Nov 10 |
Chapter 5
Problems 39, 40 Theoretical Exercises 16, 28, 30 Chapter 6
Chapter 7
|
| Homework 5 due Dec 1 | Chapter 7
Problems 30, 33, 34, 36, 41, 42, 45, 53, 56, 65, 75 Theoretical Exercises 10, 12, 19, 48, 52 Chapter 8
|