Courant Institute New York University FAS CAS GSAS

V63.0235:Probability and Statistics

Term: Spring 2011
Meeting times: Tu Th 3:30pm–4:45pm - 101 WWH
Recitation:
F 2:00 - 3:15 pm - Classroom TBD
Course Website: Probability & Statistics - Spring 2011 (and Blackboard)
Instructor: Dr. Tom LaGatta
Office: 927 WWH
Office hours: Mondays at 11am and Wednesdays at 10am
Phone: 212-992-9920
Email: lagatta@cims.nyu.edu

Prerequisites

Students who wish to enroll in V63.0235 must meet the following prerequisites:

  • V63.0122 Calculus II with a grade of C or better and/or the equivalent.

Goals and Topics

The primary goals of this course are to understand the laws of theoretical probability, and to apply them to real-world problems. The course will be full of hands-on examples, but we will not shy away from theory. In particular, this course is structured around the two major themes of the Law of Large Numbers and the Central Limit Theorem. The most important application of these ideas is statistics.

Course Details

Textbook and Materials

The Pleasures of Probability, Richard Isaac. Springer-Verlag, ISBN 0-387-94415

The Drunkard’s Walk, Leonard Mlodinow. Pantheon, ISBN 0-375-42404-0

Homework

Homework will be due every Friday by 2pm, and must be submitted in my mailbox in Warren Weaver Hall (not in class). Each week's assignment will be posted on the course website. Late homework will not be accepted for any reason; however, when I compute your final grade I will drop your lowest homework score. Homework is worth 20% of your final grade.

Programming Assignments: Probability should not be studied in a vacuum; your intuition must be honed by working with examples. The laws of probability are strongest in situations with large numbers of independent trials, such as flipping a coin 10,000 times or polling 1,500 people. Instead of doing this by hand, we will make use of the computing power available to us. As part of your homework grade, you will be expected to write a number of simple computer programs. We will be using the open-source software package, which is available to download for free from http://www.r-project.org

Reading and Writing: Probability touches on many areas of modern life, from science to finance. To place the subject matter in a broader context, there will be assigned readings each week, from the popular mathematics book The Drunkard's Walk as well as other articles. As part of your homework grade, you will be expected to write some short essays on what you read.

Exams

Quizzes
There will be a number of quizzes throughout the semester, each announced at least one week in advance. Quizzes will start at the beginning of class. These will be counted as part of your homework grade.

Midterms
There will be in-class midterm examinations on Thursday, March 3 and Thursday, April 14. I will give make-up exams only in exceptional circumstances (e.g., death in the family, outbreak of mono). Please notify me far in advance. Each midterm exam is worth 25% of your final grade.

Final
The cumulative final examination for this course is scheduled for Thursday, May 12 from 4:00pm to 5:50pm. The location will be announced in advance. The department will not be able to accommodate early finals for non-academic, non-emergency reasons. Plan your travel schedule accordingly. The final exam is worth 30% of your final grade.

Grading policy

Grades will be computed by a weighted average:

Homework 20%
Midterm 25%
Final 30%
Other 20%

Calendar

Week Topic
1 Introduction: The Law of Large Numbers and the Central Limit Theorem
2 Chapter 1 - Cars, Goats, and Sample Spaces
3 Chapter 2 - How to Count: Birthdays and Lotteries
4 Chapter 3 - Conditional Probability: From Kings to Prisoners
5 Chapter 4 - The Formula of Thomas Bayes and Other Matters
6 Chapter 5 - The Idea of Independence, with Applications
7 Chapter 7 - Random Variables, Expectations, and More About Games
8 Chapter 8 - Baseball Cards, The Law of Large Numbers, and Bad News for Gamblers
9 Chapter 9 - From Traffic to Chocolate Chip Cookies with the Poisson Distribution
10 Chapter 10 - The Desperate Case of the Gambler’s Ruin
11 Chapter 11 - Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces
12 Chapter 12 - Normal Distributions, and Order from Diversity via the Central Limit Theorem
13 Chapter 15 - Statistics: Applying Probability to Make Decisions