SIEO S4105 - Probability

Summer 2006

Syllabus (pdf)

Lecture: MW 2:30pm-4:00pm, 337 Mudd

Instructor

Rishi Talreja

Office: 313A Mudd
Email: rt2146@columbia.edu
Office hours: Monday 4:00-6:00PM

Teaching Assistant

KunSoo Park

Office: 305 Mudd
Email: kp2143@columbia.edu
Office hours: Thursday 3:00-5:00PM

Prerequisites

A working knowledge of calculus.

Text

A First Course in Probability, Sheldon Ross, 7th edition.

Course Description

This is a first course in probability for students with knowledge of elementary calculus. It will introduce the mathematics of probability theory as well as applications. The proportion of time spent on theory versus applications will be adjusted depending on the background of the students. The major topics that will be covered are the axioms or probability, conditional probability, discrete and continuous random variables, jointly distributed random variables, expectation, moment generating functions, inequalities, limit theorems, and Markov chains if time permits.

Homework

Homework will be assigned weekly in the schedule below and will be due every Monday at the beginning of class. Most problems will come from ``theoretical exercises'' in the textbook. It is ok to work together on homework. However, they must be written up individually. Solutions will be discussed either during lecture or in a separate recitation.

Exams

There will be a midterm and a final. The final exam will be cumulative, but with an emphasis on the material covered since the midterm. Both exams will be closed book.

Grading

Homework	15%
Midterm	35%
Final	50%

Schedule

The following is a rough schedule for the course. Check here for homework assignments (P corresponds to Problems and TE corresponds to Theoretical Exercises).

Date Topic Book Sections Homework

May 22 Introduction, Combinatorial Analysis 1.1-1.5 Ch. 1: P: 32, TE: 11, 12ab, 15a, 16, 19 (use induction and TE 18), 20 (Due May 31)

May 24 Axioms of Probability 2.1-2.5 Ch. 2: P: 31, 52, 55, TE: 5, 8, 14, 20 (Due June 5)

May 31 Conditional Probability, Independence 3.1-3.5

June 5 Discrete Random Variables 4.1-4.5 Ch. 3: P: 74, 83, 84, TE: 12, 18, Ch. 4: P: 13, TE: 3, 4 (Due June 12)

June 7 Discrete Random Variables 4.6-4.8 Ch. 4: P: 38, 48, 57, 60, 61, TE: 6 (very important!), 27 (Due June 14)

June 9 Continuous Random Variables 5.1-5.4

June 12 Continuous Random Variables 5.5-5.7 Ch. 5: P: 5, 6, 19, 29, 39, TE: 14 (Due June 19)

June 14 Jointly Distributed Random Variables 6.1-6.3

June 19 Midterm

June 21 Jointly Distributed Random Variables 6.4-6.5, 6.7 Ch. 6: P: 8, 12, 17, 55, TE: 16, 20 (Due June 28)

June 26 Properties of Expectation 7.1-7.2, 7.4

June 28 Properties of Expectation 7.5-7.6 Ch. 7: P: 13, 47, 55, 64, TE: 33, 22 (Due July 7)

July 5 Properties of Expectation 7.7-7.8

July 7 Inequalities, WLLN, and CLT 8.1-8.3 Ch. 7: P: 75, TE: 48, 49, 50, 53, Ch. 8: P: 1, TE: 1 (Due July 12)

July 10 SLLN and more Inequalities 8.4-8.5 Ch. 8: P: 9, 15, 19, TE: 7, 10, 13 (Due July 17)

July 12 Simulation 10.1-10.4

July 17 Stochastic Processes

July 19 Final Exam (2PM - 5PM)

Date	Topic	Book Sections	Homework
May 22	Introduction, Combinatorial Analysis	1.1-1.5	Ch. 1: P: 32, TE: 11, 12ab, 15a, 16, 19 (use induction and TE 18), 20 (Due May 31)
May 24	Axioms of Probability	2.1-2.5	Ch. 2: P: 31, 52, 55, TE: 5, 8, 14, 20 (Due June 5)
May 31	Conditional Probability, Independence	3.1-3.5
June 5	Discrete Random Variables	4.1-4.5	Ch. 3: P: 74, 83, 84, TE: 12, 18, Ch. 4: P: 13, TE: 3, 4 (Due June 12)
June 7	Discrete Random Variables	4.6-4.8	Ch. 4: P: 38, 48, 57, 60, 61, TE: 6 (very important!), 27 (Due June 14)
June 9	Continuous Random Variables	5.1-5.4
June 12	Continuous Random Variables	5.5-5.7	Ch. 5: P: 5, 6, 19, 29, 39, TE: 14 (Due June 19)
June 14	Jointly Distributed Random Variables	6.1-6.3
June 19	Midterm
June 21	Jointly Distributed Random Variables	6.4-6.5, 6.7	Ch. 6: P: 8, 12, 17, 55, TE: 16, 20 (Due June 28)
June 26	Properties of Expectation	7.1-7.2, 7.4
June 28	Properties of Expectation	7.5-7.6	Ch. 7: P: 13, 47, 55, 64, TE: 33, 22 (Due July 7)
July 5	Properties of Expectation	7.7-7.8
July 7	Inequalities, WLLN, and CLT	8.1-8.3	Ch. 7: P: 75, TE: 48, 49, 50, 53, Ch. 8: P: 1, TE: 1 (Due July 12)
July 10	SLLN and more Inequalities	8.4-8.5	Ch. 8: P: 9, 15, 19, TE: 7, 10, 13 (Due July 17)
July 12	Simulation	10.1-10.4
July 17	Stochastic Processes
July 19	Final Exam (2PM - 5PM)