University of California at
Berkeley
Dept. of Electrical Engineering
& Computer Science
EE126
Probability and Random Processes.
Spring Semester 2006
Practical information
Volume: 4 Units/Credit
Lectures:
 Tuesday, 11:0012:30 PM, 3106 ETCHEVERRY.
 Thursday, 11:0012:30 PM, 3106 ETCHEVERRY.
Discussions:
 Wednesday, 5:006:00 PM, 521 CORY.
 Thursday, 8:009:00 AM, 241 CORY.
Instructor: Martin Wainwright
 Office Hours: Tuesday 5:006:00 PM, 258 CORY; Thursday 12:301:30 PM, 258 CORY
 Email: wainwrig AT eecs DOT berkeley DOT edu
 Phone: 6431978
 Office: 263 CORY (Wireless Foundation)
Teaching assistant: Paolo Minero
 Office Hours: Monday 3:004:00 PM, 197 CORY; Wednesday 4:005:00 PM, 197 CORY
 Email: minero AT eecs DOT berkeley DOT edu
 Office: 264 CORY (Wireless Foundation)
Reader: Sahand Negahban
 Email: sahand_n AT berkeley DOT edu

 Office Hour: Monday 4:005:00 PM, 290 Cory (HKN office)

Text:
 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.
Prerequisites:
 EECS 20, and MATH 53/54 (multivariate
calculus; linear algebra) or equivalent.
Grading:
 Two midterms (20% each);
and one final exam (40%). All exams are cumulative in nature,
meaning that any topic covered in lecture, discussion or homework up to
that date can be tested.
Homeworks:
 Problem sets will be posted on the class
webpage (roughly one per week), and will be due at the
beginning of lecture of the assigned due date. 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.
Exams:
 Midterm 1: Thursday Feb 23, During class
 Midterm 2: Thursday April 13, During class
 Final Exam: Wednesday May 17, 811am
 Note: All of the exams (both midterms, and final) are
strictly noncollaborative 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 4unit 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 higherlevel 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;
longrun 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
Mon. May 15: there will be OFFICE HOUR on Monday May 15 3:004:00 PM, 197 CORY.
Mon. May 08: there will be a review session before the Final on Thurs May. 11, 2:003:30pm in SODA 306 (HP auditorium).
Mon. April 17: today's office hour is cancelled.
Thur. April 06: Midterm 2 on Tues April. 13 will cover all the material up to the end of chapter 4 (including section 4.6)..
Thur. April 06: there will be a review session before Midterm 2 on Tues April. 11, 7:008:30pm in SODA 306 (HP auditorium).
Mon. March 13: This is the schedule for next week only:
 Martin: no office hour on Tues. March 14 and Thurs. March 16
 Paolo will be giving the lectures on Tues. March 14 and Thurs. March 16
 Ming Yang will give the discussion section on Wed. March 15 and Paolo will give the discussion section on Thurs. March 16
Fri. Feb 17: there will be a review session before Midterm 1 on Tues Feb. 21, 7:008:30pm in SODA 306 (HP auditorium).
Fri. Feb 11: The makeup lecture on Frid. Feb 11 has been filmed. The video is available here
Tues. Feb 07: from this week onwards, the recitation Wed 56pm will
be held in 521 CORY, which has more seats than the original room (285 Cory).
Thurs. Feb 02: A clarification on Discussion Section on Wed. Feb. 01 has been posted to the class newsgroup. This is the schedule for next week only:
 No class on Tues. Feb. 07
 Makeup class on Frid. Feb. 10, 10:0011:30am in SODA 306 (HP auditorium)
 Martin: no office hour on Tues. Feb 7; office hours will be on Thurs. Feb. 09 at 12:30pm1:30pm and 4pm5pm.
 Paolo: no office hour on Mon. Feb 6; office hours will be on Wed. Feb. 08 at 12pm1pm and 4pm5pm.
Two umbrellas and one clipboard were found after class on Thurs. Feb 02. You can find them in Martin's office.
Tues. Jan 31: A clarification on Lecture 5 has been posted to the class newsgroup.
Thurs. Jan 19: Read Example 1.5, p. 13 of the text for background on the continuous probability model for Problem 1.6. This material will be covered on
Tuesday in class.
Wed. Jan 18: There is no discussion section on Wed. Jan. 18 (and Thurs. Jan. 19).
Tues. Jan 17: Welcome to EE126.
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Lecture schedule
Lecture No.  Date  Homework out  Homework in  Assigned Reading  Exam

1  Tues Jan 17      1.1, 1.2  

2  Thurs Jan 19  #1    1.11.3  

3  Tues Jan 24      1.3, 1.4  

4  Thurs Jan 26  #2  #1  1.41.6  

5  Tues Jan 31      1.51.6  

6  Thurs Feb 2  #3  #2  1.6, 2.1, 2.2  

7  Thurs Feb 9      2.22.4  

8  Fri Feb 10  #4  #3  2.22.5  

9  Tues Feb 14      2.62.8  

10  Thurs Feb 16    #4  2.8, 3.1  

11  Tues Feb 21      3.13.2  

Midterm #1  Thurs Feb 23  #5      Midterm1

12  Tues Feb 28      3.23.4  

13  Thurs March 2  #6  #5  3.33.5  

14  Tues March 7      3.43.6  

15  Thurs March 9  #7  #6    

16  Tues March 14        

17  Thurs March 16  #8  #7    

18  Tues March 21        

19  Thurs March 23        

SPRING BREAK  Tues March 28        

SPRING BREAK  Thurs March 30        

20  Tues April 4        

21  Thurs April 6        

22  Tues April 8        

Midterm #2  Thurs April 13        Midterm2

23  Tues April 18        

24  Thurs April 20        

25  Tues April 25        

26  Thurs April 27        

27  Tues May 2        

28  Thurs May 4        

29  Tues May 9       

Final Exam  Wed May 17        Final

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Discussion Sections
Discussion Section on Wed March 8, Thurs March 9: [pdf]. Solutions: [pdf].
Discussion Section on Wed March 15, Thurs March 16: [pdf]. Solutions: [pdf].
Discussion Section on Wed March 22, Thurs March 23: [pdf]. Solutions: [pdf].
Discussion Section on Wed April 05, Thurs April 06: [pdf]. Solutions: [pdf].
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Homeworks
Homeworks are due Friday by 4pm. You can drop your homework in the EE126 box in 240 Cory. Early assignment (e.g. Thurs in class) are fine, but no late homeworks will be accepted
Homework #1: [pdf] [ps]. Solutions: [pdf] [ps].
Homework #2: [pdf] [ps]. Solutions: [pdf] [ps].
Homework #3: [pdf] [ps]. Solutions: [pdf] [ps].
Homework #4: [pdf] [ps]. Solutions: [pdf] [ps].
Midterm review: [pdf] [ps]. Solutions: [pdf] [ps]..
Midterm 1 solutions: [pdf] [ps]. Histogram [jpg].
Homework #5: [pdf] [ps]. Solutions: [pdf] [ps].
Homework #6: [pdf]
[ps]. Solutions: [pdf] [ps].
Homework #7: [pdf]
[ps]. Solutions: [pdf] [ps].
Homework #8: [pdf]
[ps]. Solutions: [pdf] [ps].
Midterm review: [pdf] [ps]. Solutions: [pdf] [ps]..
Homework #9: [pdf]
[ps]. Solutions: [pdf] [ps].
Midterm 2 solutions: [pdf] [ps]. Histogram [jpg].
Homework #10: [pdf]
[ps]. Solutions: [pdf] [ps].
Homework #11: [pdf]
[ps]. Solutions: [pdf] [ps].
Final review: [pdf]
[ps]. Solutions: [pdf] [ps].
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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 LeonGarcia: Probability and Random Processes for Electrical Engineering , Second edition, AddisonWesley, 1992.
Sheldon Ross: A First Course in Probability , Fifth edition, Prentice Hall, 1998