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.
Instructor
Dr. Rudolf RiediAssistants
Duncan Hall 2025, 713 / 348 3020,
Office Hours: Tu 4-6pm and W 10-12am (DH 2025), or by appointment
Rui Castro
Duncan Hall 2122, 713 / 348 2821
Office Hours: Th 3-5pm (DH 2122), or by appointment
Shriram Sarvotham
Duncan Hall 2120, 713 / 348 2600
Office Hours Th 5-7pm (DH 2120), or by appointment
Time and Place
Wednesday Friday 9:00 - 10:15 am, AL (Abercrombie Lab) 126
For current updates check the official Rice page
Outline
Textbook
Further suggested readingH. 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.
Stark & Woods, Wond & Hayek, and Papoulis are on reserve
at Fondren Library
Grading
15% QUIZ
30% Midterm EXAM
30% Last EXAM
15% Homework
10% Notes and participation in class
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]
Classes
This doubles as a calendar for the course. Note that a * indicates a Monday lecture.
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 | Reading: Stark&Woods (2002) | |
August 29 | Orientation, history | |
September 5 | Probability space | pp 1-11mid |
September 7 | Discrete and Continuous Proba Spaces | pp 11-15 |
September 12 | Borel sets, Conditional Prob., Bayes | pp 16-24; Combinatorics 24-32 |
September 14 | Independence, Random variables, CDF | pp 58-80 |
September 19 | pdf, expectation, functions of one r.v. | pp 169-171, 116-134 |
September 21 | Expect. (examples), E[g(X)], variance | pp 172-175, 192-196 |
September 26 | Bernoulli trials, Joint distributions, Marginals, Independent r.v. | pp 32-44, 88-99 |
Up to here: Material for Quiz | ||
September 28 | Functions of two r.v., Sums and Products, Covariance | pp 134-152 |
October 3 | Joint Gaussian Pair, Stieltjes integral | pp 100-102, 80-88 |
October 5 | Conditional distribution and expectation | pp 103-108, 183-192 |
October 8 (Monday 9:30-10) | Quiz | |
October 10 | Discussion of Quiz, E[Y|X]: continuous | pp 183-192 |
October 12 | E[Y|X]: projection, MMSE; Gaussian linear prediction | pp 552-555, 556-558 |
October 15 (for your information) | Fallbreak | |
October 17 (!) | Characteristic function | pp 216-225 |
October 19 | Multivariate Gaussian, Covariance, Inequalities | pp 269-277, 205-210 |
October 24 | Conv. of functions (pointwise, uniform ,L2) | pp 375-376 |
October 26 | Convergence of r.v. (as, ms, ip, D) | pp 377-383 |
* October 29 (instead Nov 2) | Comparing convergence, Martingales | pp 225-230, 383-387 |
From beginning to here: Material for Test 1 | ||
October 31 | Discussion of Homework and Convergence | |
November 7 | Limit theorems (Martingales and LLN, CLT, Chernoff bound) | 383-387, 225-230, 214-216 |
November 9 | Random Processes, basics, examples | 401-407 |
November 14 | Auto-correlation, Stationarity | |
November 16 | Renewal processes, Poisson | 408-414 |
* November 19 | Consistency: Gaussian Processes, Markov | 418-421, 421-430 |
November 21 | Chapman-Kolmogorov, Spectral density | 429-430, 348-354 |
November 23 | Thanksgiving | |
November 28 | Gauss Markov, homework | 362-365, 421-423, 429-430 |
November 30 | Auto-corr of wss Markov; Mean square calculus | 430, Ex 9.1-4 p 565; pp 487-497 |
From Test 1 (Nov 7) to here: Material for Test 2 | ||
December 5 | Discussion of homework and test 1 | |
December 7 | Linear Systems with random input, White Noise |
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]
Homework
(tex-source and solutions restricted to Rice University)
This
file is needed to latex the source.
Homework sheet | Due date (in class) | Solutions |
Problem Set 1 [ps] [pdf] [tex] | Sept 14, 2001 | handed out Sept 21 [ps] [pdf] [tex] |
Problem Set 2 [ps] [pdf] [tex] | Sept 21, 2001 | handed out Sept 28 [ps] [pdf] [tex] |
Problem Set 3 [ps] [pdf] [tex] | Sept 28, 2001 | handed out Oct 3 [ps] [pdf] [tex] |
Problem Set 4 [ps] [pdf] [tex] | Oct 3, 2001 | handed out Oct 5 [ps] [pdf] [tex] |
Problem Set 5 [ps] [pdf] [tex] | Oct 19, 2001 | handed out Oct 26 [ps] [pdf] [tex] |
Problem Set 6 [ps] [pdf] [tex] | Oct 26, 2001 | handed out Oct 31 [ps] [pdf] [tex] |
Problem Set 7 [ps] [pdf] [tex] | Oct 31, 2001 | handed out Nov 2 [ps] [pdf] [tex] |
Problem Set 8 [ps] [pdf] [tex] | Nov 21, 2001 | handed out Nov 28 [ps] [pdf] [tex] |
Problem Set 9 [ps] [pdf] [tex] | Nov 30, 2001 | handed out Nov 30 [ps] [pdf] [tex] |
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.
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]
Quiz (15% towards the grade) | October 8 | In class, 30 min, (open: only two hand-written pages ) |
Test 1 (30%) | Handed out: October 31. Due: November 14. | Take home, 3 hours, (open notes) |
Test 2 (30%) | Handed out: November 30. Due December 7 | Take home, 4 hours (open books) |