University of California at
Berkeley
Dept. of Electrical Engineering
& Computer Science
EE126
Probability and Random Processes
Fall Semester 2007
Updates and Announcements
 Ali G wishes you good luck on your final!
 Answers and hints to the most recent discussion section notes have been posted in the Discussion section.
 Solutions to both practice finals have been posted. There have been a few updates, so if you have a question on one of the solutions, be sure you have the latest revision.
 The MIT 6.041 site has review slides for postMT2 material. They also have all their previous tests if you want more practice questions. However, you should make previous EE126 exams your highest study priority.
 Office hours this week:
Zile: Tuesday 1011am in 197 Cory
Matt: Tuesday 35pm, Wednesday 35pm in 197 Cory
Prof. Wainwright: Tuesday 1:102:10pm, Wednesday1:102:10pm in 263 Cory
 Here is a bonus problem on lossy compression theory. You can tackle it with what you've learned in EE126.
 Book solution link was moved to the Useful References section.
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Practical Information
Course syllabus: [pdf][ps]
Volume: 4 Units/Credit
Lectures:
 Tuesday, 3:305:00 PM, 247 CORY.
 Thursday, 3:305:00 PM, 247 CORY.
Discussions:
 Monday, 4:005:00 PM, 293 CORY.
 Wednesday, 10:0011:00 AM, 293 CORY.
 Friday, 9:0010:00 AM, 3102 Etcheverry
Instructor: Martin Wainwright
 Office Hours: Tu 56pm, Th 12:301:30pm, 258 Cory
 Email: wainwrig AT eecs DOT berkeley DOT edu
 Phone: 6431978
 Office: 263 CORY (Wireless Foundation)
Teaching assistants: Matt Johnson and Zile Wei
 Office Hours: Matt: M 121, W 23 in 197 Cory; Zile: Tue 1011am in 197 Cory
 Email: mattjohnson AT berkeley DOT edu, zile AT eecs DOT berkeley DOT edu
 Office: TBD
Reader: TBD
 Email: TBD

 Office Hour: TBD

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:
 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.
Homeworks:
 Problem sets will be posted on the
class webpage (roughly one per week), and will be due in the Cory Hall
box at 6pm on the date specified on the problem set. 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, Oct 4
 Midterm 2: Thursday, Nov 15
 Final Exam: TBD
 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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Discussion Sections
Discussion notes are the same across section times. All files linked are PDF files.
 Week 1 [pdf]: Sets, Probabilistic Models
 Week 2 [pdf]: Conditional and Total Probability, Independence
 Week 3 [pdf]: Bayes' Rule, Counting, Random Variables
 Week 4 [pdf]: Marginal and Joint PMFs, Expectation, Variance
 Week 5: Midterm Review
 Week 6 [pdf], Hints [pdf]: Continuous RVs
 Week 7 [pdf], Hints [pdf]: Continuous RVs continued, Multiple RVs, Order Statistics
 Week 8 [pdf], Hints [pdf]: Transforms, Iterated Expectation and Variance, Random Sums
 Week 9 [pdf], Hints [pdf]: Conditional Expectations, Estimators, LLSE, Covariance
 Week 10 [pdf], Hints [pdf]: Bernoulli Process (in notes) and Midterm Review
 Week 11: Poisson Process (discussed HW problem 10.1)
 Week 12 [pdf], Hints [pdf]: Random Incidence, Markov Chains
 Week 13 [pdf], Hints [pdf]: Markov Chains, Chebyshev Inequality
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Homeworks
 Problem Set 1: [pdf]; Solutions: [pdf]
 Problem Set 2: [pdf]; Solutions: [pdf]
 Problem Set 3: [pdf]; Solutions: [pdf]
 Problem Set 4: [pdf]; Solutions: [pdf]
 Midterm 1 Review: [pdf]; Solutions: [pdf]
 Problem Set 5: [pdf]; Solutions: [pdf]
 Problem Set 6: [pdf]; Solutions: [pdf]
 Problem Set 7: [pdf]; Solutions: [pdf]
 Problem Set 8: [pdf]; Solutions: [pdf]
 Problem Set 9: [pdf]; Solutions: [pdf]
 Midterm 2 Review: [pdf]; Solutions: [pdf]
 Problem Set 10: [pdf]; Solutions: [pdf]
 Problem Set 11: [pdf]; Solutions: [pdf]
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Exams
Current Semester
Midterm 1
 Review: [pdf]; Solutions: [pdf]
 Exam: [pdf]; Solutions: [pdf]
 Statistics: [pdf]
Midterm 2
 Review: [pdf]; Solutions: [pdf]
 Exam: [pdf]; Solutions: [pdf]
 Statistics: [pdf]
Joint Scatter: [pdf]
Previous Semesters
 Midterm 1 Fa06: [pdf]; Solutions: [pdf]
 Midterm 1 Sp06: [pdf]; Solutions: [pdf]
 Midterm 2 Fa06: [no link]; Solutions: [pdf]
(NOTE: the solution to the last problem is incomplete, since it doesn't find var(X^2), so check the HW9 solutions instead)
 Midterm 2 Sp06: Same as MT2 review problems.
 Final Fa06: [pdf]; Solutions: [pdf]
 Final Sp06: [pdf]; Solutions: [pdf]
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Useful References
Don't forget that there are solutions to the unstarred book problems online. Note that the file only contains unstarred solutions, since the starred solutions are in the book.
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