University of California, Berkeley
Electrical Engineering and Computer Sciences Department

Course Details |Course Outline | Course Handouts | Homework | Announcements | Lecture Notes | Discussions


Probability and Random Processes

Tue. and Thu.: 12:30 am. - 2:00 pm
247 Cory

Prerequisite: EE20 

Text: "Introduction to Probability" by Bertsekas and Tsitsiklis

Discussion Sections:
Tuesday,  4:00 - 5:00 pm, 293 Cory
Thursday, 9:00 - 10:00 am, 241 Cory

Professor Anant Sahai
267 Cory Hall

Office Hours:
Monday, Tuesday, 2:00-3:00 pm and by appointment

258 Cory Hall

Teaching Assistant:
Cheng Chang
Office Hours:
Friday 12:00 – 2:00 pm

197 Cory Hall

Reader’s Office Hour:
Monday 5:00 – 6:00  pm

531 Cory Hall


  • Welcome to EE126
  • Exam schedule: Midterm 1 (September 29th) and Midterm 2 (November 10th)
  • Final:   Monday 12/19/05 12:30-3:30pm (open textbook only, no additional sheets or notes) 
  • Correction on Problem 18, hw1 : Alice and Bob have 2n+1 FAIR coins, each with probability of a head equal to ½.
  • Correction on Problem 10, hw2 : Let N be a NON-NEGATIVE integer-valued random variable.
  • TA’s new office hour: Friday  12:00- 2:00
  • Practice Midterm and solutions online, report errors to the TA
  • Homework3 solutions (Problem A. (b) corrected) online. Thanks to L. W.
  • Extra office hour: 1:00- 3:00 pm, November 9th
  • No discussion sessions in the week of Thanksgiving
  • Problem 4 is dropped from Homework 11, check out the new homework assignment
  • No office hour this week (Nov. 28th, 29th)
  • New solutions to HW11        Midterm histograms
  • Some corrections on Homework 12: Due Thursday Dec 8th rather than Tue Dec 6th
  • Review session:  5:00-7:00pm, Wednesday Dec 14th  293 Cory
  • Practice Final     Solutions        Final Exam (SP’05)
  • Corrections on the Solutions to HW 12
  • Final Exam Schedule:  MONDAY, DECEMBER 19, 2005  1230-330P, C125 CHEIT
  • Final Exam       Solutions

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Course Details:

  • Text: Introduction to Probability by Bertsekas and Tsitsiklis. Available in campus bookstore.  You will be expected to do the reading on your own and are strongly urged to try your hand at every single problem in the textbook. Solutions to the book problems are available online
  • Grading: Homeworks (20%), Two Midterms (40%), Final (40%). All exams are cumulative and any topics covered in readings, lecture,  discussions, or homework to that point can show up on an exam.
  • Homeworks: Homeworks will show up on the class website and will be due every week at the beginning of Tuesday lecture.  Make a photocopy of your homework and turn in that copy. Solutions will appear online shortly, and students are required to grade their own homework, and email the itemized grades to the TA before the next homework is due. If you do not grade your own homework, we will assume that you want a zero for that assignment. Students are encouraged to collaborate on homework and groups of one to three students may identify themselves on their homeworks, but need to write up their solutions individually.
  • Exams are not collaborative and cheating will not be tolerated as per the department's Academic Dishonesty Policy.
  • Midterms: Midterm 1: Thu Sep 29th, in class. Midterm 2: Thu Nov 10, in class. The preceding Tuesdays will be in-class review sessions. The discussion section will cover some practice midterm questions. Both midterms are closed book with one sheet of notes   permitted, that must be turned in with the exam.
  • Final: As per the exam schedule, Dec 19th 12:30pm at the TBA location. A review session will be scheduled. Open book, but no notes are permitted.
  • Prerequisites: EECS 20 (absolute must), and Math 53/54 or equivalent.
  • Other: EECS 126 at Berkeley is similar to the course 6.041 at MIT6.041, The difference is that our 126 covers more material at a slightly more intense level than our MIT counterpart. Even so, you should find the MIT course website a useful resource for your studying.


This course will build on EECS 20 and will help give you the tools and understanding you will need to get to senior/grad level classes like 121, 226a, 224ab, etc. EECS 120 (Signals and Systems) is not required for this course and gives a complementary set of tools needed for

advanced material, especially in the area of communications. In addition:


l        We want you to master the material covered in this class and to get a good grade. We understand that different students have different ways of learning, and so extra credit can be made available for a range of activities: from scribing good lecture notes for sharing with the class (make them in LaTeX format with eps figures) to doing projects that demonstrate deeper understanding.

l        To understand this material well, you have to work out problems and explore on your own. The assigned homework is the bare minimum --- you should be working out book problems, trying to stump your classmates with puzzles, as well as playing with coins, cards, and dice. You are strongly encouraged to form study groups for this course.

l        While helping your classmates learn the material and getting help from upperclassmen who have taken the class is a good idea, cheating on exams is dishonorable and will be severely punished.

l        Give feedback to us if you have comments or questions.

l        HKN is your friend. Take advantage of the free tutoring.

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Course Outline: (This is the goal, although the schedule may be adjusted depending on class interest, performance, etc...)

Aug 30 Sep 1: Administrivia and begin Chapter 1. Basics of probability and the concept of independence.


Sep 6, 8: Chapter 1 continued: conditioning and counting. These lectures will be given by the GSI.


Sep 13, 15, 20: Chapter 2: discrete random variables.


Sep 22: Start Chapter 3: continuous random variables.


Sep 27, 29: Review Session (GSI) and Midterm. The  assigned homework this week is to do the midterm again at home.


Oct 4, 6, 11: Continue Chapter 3. Extra emphasis (beyond the textbook) on mixed continuous and discrete random variables.


Oct 13: Slack in case we are falling behind or can jump ahead.


Oct 18, 20, 25, 27: Chapter 4. Additional material will be presented in class giving a geometric and linear algebra perspective on the bivariate normal distribution.


Nov 1, 3: Chapter 5: Bernoulli and Poisson arrival processes.


Nov 8, 10: Review Session (GSI) and Midterm. The assigned homework this week is to do the midterm again at home.


Nov 15: Advanced topics from Chapter 5.


Nov 17, 22, 29: Chapter 6: Markov Chains. Additional material will be presented in class giving linear algebra tools for understanding Markov chains.


Dec 1, 6, 8: Chapter 7: Laws of large numbers and bounding


The discussion sections each week will review background material and supplement lecture, but mostly will be showing how to solve problems that apply the material covered in lecture.

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Lecture Notes:

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 Created by Danijela Cabric on January 19, 2005.
 Last updated 01/17/05