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, 11:00--12:30 PM, 3106 ETCHEVERRY.
Thursday, 11:00--12:30 PM, 3106 ETCHEVERRY.

Discussions:

Wednesday, 5:00--6:00 PM, 521 CORY.
Thursday, 8:00--9:00 AM, 241 CORY.

Instructor: Martin Wainwright

Office Hours: Tuesday 5:00--6:00 PM, 258 CORY; Thursday 12:30--1:30 PM, 258 CORY
Email: wainwrig AT eecs DOT berkeley DOT edu
Phone: 643-1978
Office: 263 CORY (Wireless Foundation)

Teaching assistant: Paolo Minero

Office Hours: Monday 3:00--4:00 PM, 197 CORY; Wednesday 4:00--5:00 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 4:00--5:00 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.

Pre-requisites:

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, 8-11am

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 .

Back to top


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).
  • Back to top


    Updates and Announcements

  • Mon. May 15: there will be OFFICE HOUR on Monday May 15 3:00--4:00 PM, 197 CORY.

  • Mon. May 08: there will be a review session before the Final on Thurs May. 11, 2:00-3:30pm 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, 7:00-8:30pm in SODA 306 (HP auditorium).

  • Mon. March 13: This is the schedule for next week only:

  • Fri. Feb 17: there will be a review session before Midterm 1 on Tues Feb. 21, 7:00-8:30pm in SODA 306 (HP auditorium).

  • Fri. Feb 11: The make-up lecture on Frid. Feb 11 has been filmed. The video is available here

  • Tues. Feb 07: from this week onwards, the recitation Wed 5-6pm 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:
  • 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.
  • Back to top


    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

    ---

    1.1--1.3

    ---

    3

    Tues Jan 24

    ---

    ---

    1.3, 1.4

    ---

    4

    Thurs Jan 26

    #2

    #1

    1.4--1.6

    ---

    5

    Tues Jan 31

    ---

    ---

    1.5--1.6

    ---

    6

    Thurs Feb 2

    #3

    #2

    1.6, 2.1, 2.2

    ---

    7

    Thurs Feb 9

    ---

    ---

    2.2--2.4

    ---

    8

    Fri Feb 10

    #4

    #3

    2.2--2.5

    ---

    9

    Tues Feb 14

    ---

    ---

    2.6--2.8

    ---

    10

    Thurs Feb 16

    ---

    #4

    2.8, 3.1

    ----

    11

    Tues Feb 21

    ---

    ---

    3.1--3.2

    ----

    Midterm #1

    Thurs Feb 23

    #5

    ---

    ---

    Midterm1

    12

    Tues Feb 28

    ---

    ---

    3.2--3.4

    ----

    13

    Thurs March 2

    #6

    #5

    3.3--3.5

    ----

    14

    Tues March 7

    ---

    ---

    3.4--3.6

    ----

    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

    Back to top


    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].

  • Back to top


    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].

  • Back to top


    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.

  • Back to top


    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