University of California at Berkeley
Dept. of Electrical Engineering & Computer Science

Probability and Random Processes.

Fall Semester 2006

Practical information

Course syllabus: [pdf][ps]

Volume: 4 Units/Credit


Tuesday, 3:30--5:00 PM, 247 CORY.
Thursday, 3:30--5:00 PM, 247 CORY.


Monday, 4:00--5:00 PM, 293 CORY.
Friday, 9:00--10:00 AM, 531 CORY.

Instructor: Martin Wainwright

Office Hours: Tu/Th 5-6pm 258 Cory
Email: wainwrig AT eecs DOT berkeley DOT edu
Phone: 643-1978
Office: 263 CORY (Wireless Foundation)

Teaching assistant: Daniel Preda

Office Hours: Cory 197: Wed 9-10, Thu 2:30-3:30
Email: dpreda AT eecs DOT berkeley DOT edu
Office: 592 Soda

Reader: TBD

Email: TBD
Office Hour: TBD


Introduction to Probability by Bertsekas and Tsitsiklis. Available at the campus book store. In addition to attending lectures and discussions, doing problems and reading the textbook outside class will be an integral part of the learning process.


EECS 20, and MATH 53/54 (multivariate calculus; linear algebra) or equivalent.


Homework (15%), two midterms (20% each), and one final exam (45%). All exams are cumulative in nature, meaning that any topic covered in lecture, discussion or homework up to that date can be tested.


Problem sets will be posted on the class webpage (roughly one per week), and will be due in the Cory Hall box. Late homeworks will not be accepted. If they chose, after attempting the problems on an individual basis, students can discuss homework assignments in groups of at most three. However, each student must write up his/her own solutions individually, and must explicitly name any collaborators at the top of the homework.


Midterm 1: Thursday, Oct 5; Solutions: [pdf][ps]
Midterm 2: Thursday, Nov 16; Solutions: [pdf][ps]
Final Exam: TUESDAY, DECEMBER 19, 2006 1230-330P

Note: All of the exams (both midterms, and final) are strictly non-collaborative in nature. Any form of cheating will not be tolerated as per the Department's Academic Dishonesty Policy .

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Course description

This course is a 4-unit course that provides an introduction to the basics of probability and random processes. This material is central to many fields in electrical engineering and computer science, including statistical signal processing, communications, control theory, and networking. It builds on the foundation of EE 20, and provides necessary background for higher-level courses, work and research. The material in EE 120 is complementary to the material covered in this course.

  • Basics of probability (Chapter 1): sets, probabilistic models, sample spaces, conditioning, Bayes' rule, independence etc. (Time: approx. two weeks).

  • Discrete random variables (Chapter 2): definitions, examples, mass functions, expectation, mean, variance etc. (Time: approx. two weeks).

  • General random variables (Chapter 3): continuous variables, density functions, conditioning, normal variables etc. (Time: approx. two weeks).

  • Further topics (Chapter 4): transforms, convolution, conditional expectation, least squares, bivariate normal (Time: approx. two to three weeks).

  • Bernoulli and Poisson processes (Chapter 5): definitions, examples, properties (Time: approx. one to two weeks).

  • Markov chains (Chapter 6): discrete time chains; classification; long-run behavior; absorption. (Time: approx. one to two weeks).

  • Limits of random variables (Chapter 7): inequalities, law of large numbers, central limit theory (Time: approx. one to two weeks).
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    Updates and Announcements

    Dec 12, 12:00 AM: Solutions to final exam review: [pdf]

    Dec 08, 02:30 PM: Office hours next week Fri Dec 15, 4-6 PM Cory 197. You can pick up PS 11 then.

    Dec 08, 02:30 PM: Final exam review session Tue Dec 12, 8-10 PM in Soda 306

    Dec 08, 02:30 PM: Practice problems posted: [pdf][ps]

    Nov 21, 05:45 PM: Midterm 2 solutions: [pdf][ps]

    Nov 16, 10:30 AM: Uptaded solution to problem 6.2: [pdf]

    Nov 15, 12:00 PM: Solutions to the practice midterm: [pdf]

    Nov 08, 11:00 PM: Practice midterm posted: [pdf][ps]

    Oct 23, 12:00 PM: Due to a conference this week, there are some slight changes in section / office hours: 1. Today, Mon, I might be a bit late for my section - if I don't show up on time, don't panic :) 2. The office hours from Wed are moved to Tue 1-2 PM, and the office hours from Thu are moved on Fri 11-12.

    Oct 11, 04:45 PM: Midterm 1 solutions: [pdf][ps].

    Oct 04, 11:00 AM: I truly appologize for missing the office hours today. As a makeup, I will be in the OH room (Cory 197) from 3-5 PM today. If I'm not there, it means I'm in Prof. Wainwright's office, look for me there.

    Oct 03, 11:00 PM: Practice midterm solutions posted [pdf].

    Sep 26, 01:00 PM: Practice midterm posted [pdf].

    Sep 05, 06:30 PM: TA office hours in Cory 197, Wed 9-10 & Thu 2:30-3:30

    Aug 30, 08:30 PM: First three sections of the textbook have been posted online for those students who don't have the book: [pdf]

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    Lecture schedule

    Lecture No.


    Homework out

    Homework in

    Assigned Reading



    Tues Aug 29






    Thurs Aug 31

    PS1 [ps]





    Tues Sep 5



    1.3, 1.4



    Thurs Sep 7

    PS2 [ps] [pdf]


    1.3, 1.4



    Tues Sep 12



    1.5, 1.6



    Thurs Sep 14

    PS3 [ps] [pdf]


    1.5, 1.6



    Tues Sep 19





    Thurs Sep 21

    PS4 [ps] [pdf]





    Tues Sep 26





    Tues Sep 28





    Tues Oct 3





    Thurs Oct 5

    PS5 [ps] [pdf]




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    Discussion Sections

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    Problem Set 1: [ps]; Solutions: [pdf]

    Problem Set 2: [ps] [pdf]; Solutions: [pdf]

    Problem Set 3: [ps] [pdf]; Solutions: [pdf]

    Problem Set 4: [ps] [pdf]; Solutions: [pdf]

    Problem Set 5: [ps] [pdf]; Solutions: [pdf]

    Problem Set 6: [ps] [pdf]; Solutions: [pdf]

    Problem Set 7: [ps] [pdf]; Solutions: [pdf]

    Problem Set 8: [ps] [pdf]; Solutions: [pdf]

    Problem Set 9: [ps] [pdf]; Solutions: [pdf]

    Problem Set 10: [ps] [pdf]; Solutions: [pdf]

    Problem Set 11: [ps] [pdf]; Solutions: [pdf]

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    Course newsgroup

  • You can post your questions about course material and homeworks on the EE126 Newsgroup. Please see here for instructions on connecting and using the newsgroup. Note that a special procedure is required to gain access from outside the UCB computer system.

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    Useful references

  • Professor Walrand's notes for EE126

  • Alberto Leon-Garcia: Probability and Random Processes for Electrical Engineering , Second edition, Addison-Wesley, 1992.

  • Sheldon Ross: A First Course in Probability , Fifth edition, Prentice Hall, 1998