Introduction to Random Processes

 ELEC 533, Fall 2000

 Rice University

This course covers the basic concepts of probability theory and random processes
at a fairly rigorous level and discusses applications such as to Digital Communication Systems.


Dr. Rudolf Riedi
Duncan Hall 2025, 713 / 348 3020,
Office Hours: Tuesday 1-2 pm and 5-6 pm, or by appointment
Ramesh Neelamani
Duncan Hall 2121, 713 / 348 3230
Office Hours: Monday 1:45-2:45, 5-6 pm, or by appointment

Vinay Keshavan Bharadwaj
Duncan Hall 2047, 713 / 348 2471
Office Hours: Thursday 1-3 pm, or by appointment

Time and Place

Wednesday Friday   9:00 - 10:15 am, AL (Abercrombie Lab) 126

[Outline]  [Textbooks]  [Grading]  [Reading assignment]  [Homework problems and solutions]  [Tests] 


Review of Basic Probability Theory (incl. conditional probability)
QUIZ (one sheet or two pages of personal notes)
Random Vectors and Sequences (joint distributions, limiting laws)
Random Processes (wide sense stationarity, Poisson, Markov, Wiener processes)
Midterm EXAM (open-notes, closed-books)
Spectral properties, Linear Systems, White noise, KLT
Final EXAM (open-notes)


  • H. Stark and J. Woods, `Probability, Random Processes, and Estimation Theory for Engineers'.
    The course will closely follow this book; it is available at the campus bookstore.
  • Further suggested reading Standard references on Probability Theory

    Stark & Woods, Wond & Hayek, and Papoulis are on reserve at Fondren Library


    15%  QUIZ
    30%  Midterm EXAM
    30%  Last EXAM
    15%  Homework
    10%  Notes and participation in class

    This part will be updated during the semester helping you to identify the material covered in class and where to find further reading.
    To get an idea what will be discussed during the whole course and what is likely to be covered in the quiz and tests please have a look at last years course schedule
    Covered material
    Covered material Reading: Stark&Woods (1994)
    August 29 Orientation, history
    August 30 Probability space pp 1-12
    September 1 Borel sets read ahead: pp 21-28
    September 6 Conditional Prob., Bayes, Independence pp 13-21
    September 8 Bernoulli trials, Random variables pp 28-36, 52-56
    September 13 CDF, pdf, functions of one r.v. pp 56-60, 66-74, 106-122
    September 15 Expectation, variance pp 160-165, 178-180
    September 20 Expect. (examples), Joint distributions pp 74-87
    September 22 Joint distributions, Marginals, Independent r.v. pp 88-92
    September 25 Functions of two r.v., Sums and Products pp 122--140
    Up to here: Material for Quiz
    September 29 Conditional distribution, discrete pp 74-81
    October 4 Discussion on Quiz, Conditional expectation pp 170-178
    October 6 Cond expect, continuous pp 170-178
    October 11 Correlation, jointly Gaussian r.v. pp 182-193
    October 13 Estimation of r.v. pp 296-303
    October 18 Characteristic function pp 204-213, 258-261
    October 20 Multivariate Gaussian, Covariance, Inequalities pp 261-263, 248-258, 194-198
    October 25 Conv. of functions (pointwise, uniform ,L2) and r.v. (as, ms) pp 348-353
    October 27 Convergence of r.v. (as, ms, ip, D) pp 348-357
    November 1 Limit theorems (LLN, CLT) pp 357-362, 213-218
    From beginning to here: Material for Test 1
    November 3 Random Processes, basics pp 318-326, 371-376
    November 6 R.P. examples, Auto-correlation, Stationarity pp 326-336
    November 8 Renewal processes, Poisson pp 376-386
    November 15 Poisson, Markov, Gaussian Processes pp 377-386, 391-396
    November 17 Consistency, Brownian motion pp 330-331, 386-391, 396-399
    November 22 Colored noise, Gauss Markov, Spectral density 391-393, 395-399
    November 24 Thanksgiving
    November 29 (Cross) Spectral density, mean square continuity pp 465-472, 419-422
    December 1 Mean square calculus, White Noise pp 422-430
    From Fallbreak to here: Material for Test 2
    December 6 Linear Systems with random input pp 399-404, 433-437
    December 8 KL pp 450-457

    Homework (tex-source for graders only)
    Homework sheet Due date (in class) Solutions
    Problem Set 1 [tex] Sept 13, 2000 handed out Sept 20 Set 1 [tex]
    Problem Set 2 [tex] Sept 20, 2000 handed out Sept 25 Set 2 [tex]
    Problem Set 3 [tex] Sept 27, 2000 handed out Sept 29 Set 3 [tex]
    Problem Set 4 [tex] Oct 13, 2000 handed out Oct 13 Set 4 [tex]
    Problem Set 5 [tex] Oct 120, 2000 handed out Oct 27 Set 5 [tex]
    Problem Set 6 [tex] Oct 27, 2000 handed out Nov 1 Set 6 [tex]
    Problem Set 7 [tex] Nov 3, 2000 handed out Nov 10: Neelsh
    Problem Set 8 [tex] Nov 8, 2000 handed out Nov 10 Set 8 [tex]
    Problem Set 9 [tex] Nov 29, 2000 handed out Dec 5 Set 9 [tex]
    Problem Set 10 [tex] Dec 1, 2000 handed out Dec 1 Set 10 [tex]

    Late Homework Policy

    Homework is due at the beginning of class on the due date. After the due date, but before solutions are handed out, homework can be turned in for 50% credit. In this case, please slip your homework under the door of DH 2025, or DH 2121, or bring it to class. After solutions are handed out, 0% credit will be issued. You are encouraged to work in groups for homeworks but you will hand in your own solution which you are expected to understand.

    Quiz (15% towards the grade) Monday, October 2nd, 9:00 - 9:45 am (open: only two personal pages )
    Midterm (30%) Handed out Nov 10 (Duncan 2121), due Nov 15 midnight. take home, 3 hours, open notes
    Last Test (30%) Handed out Dec 1, due Dec 8 noon take home, 7 days, 4 hours (open books)

    Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disabled Student Services in the Ley Student Center.
    August 7, 2000.  Dr. Rudolf Riedi