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
Bhaskar Nallapureddy
Duncan Hall DH1040, 713 / 348 3579,
Office Hours: MW 4:30pm-5:30pm, or by appointment
Mohammed Ahamed KhanTime and Place of Classes
Duncan Hall DH2113, 713 / 348 2776,
Office Hours: TTh 10:30-11:30am, or by appointment
Wednesday Friday 8:45 - 10:00 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 28 | Orientation, history | |
August 30 | Probability space | pp 1-15, Combinatorics: 24-31 |
September 4 | Sigma-Algebra, Borel sets, continuous spaces | read pp 16-24 |
September 6 | Bayes, Independence, Random variables | pp 58-68 |
September 9 (instead Wed) | CDF, density (pdf), functions of one r.v. | pp 68-80, 129 |
September 13 | HW 1, expectation, E[g(X)] | pp 116-134, 169-175 |
September 18 | Moments, Independent experiments | pp 192-196, 32-44 |
September 20 | Joint distributions, Marginals, Independent r.v. | pp 88-99 |
Up to here: Material for Quiz | ||
September 25 | Functions of two r.v., Sums and Products, Covariance | pp 134-152 |
September 27 | Stieltjes integral, generalized density (Dirac) | |
October 2 | Conditional density and expectation E[Y|X] | pp 80-88, 103-108 |
October 4 | E[Y|X]: rules, several variables | pp 183-192 |
October 9 | Characteristic function, Cumulants | pp 216-225 |
October 11 | Multivariate Distributions, Covariance | pp 269-277 |
October 16 | Jointly Gaussian: distribution and estimation | pp 269-277, 556-561 |
October 18 | Convergence of functions and random variables | pp 375-379 |
October 23 | Inequalities, Comparison of Convergence | pp 205-210, 375-379 |
October 25 | Comparing convergence, Martingales | pp 225-230, 383-387 |
Monday October 28 | Limit theorems (Martingales and LLN) | pp 383-387, 225-230, 214-216 |
October 30 |
Limit theorems (CLT, Chernoff, LDP) |
|
From beginning to here: Material for Test 1 |
||
November 1 | NO CLASS | November 6 | Random Processes, basics, examples | pp 401-407 |
November 8 | Auto-correlation, Stationarity | pp |
Monday November 11 (instead 13) | Renewal processes, Poisson | pp 408-414 |
November 13 | NO CLASS |
|
November 15 | NO CLASS | |
Monday November 18 (instead 15) | Poisson properties | pp 408-416 |
November 20 | Consistency: Gaussian Processes, Markov | pp 418-421, 421-430 |
November 22 | Chapman-Kolmogorov, | pp 429-430 |
Monday November 25 (Thanksgiving) | Spectral density | 348-354 |
November 27 | Mean square calculus | pp 487-497 | November 29 | Thanksgiving |
From Test 1 to here: Material for Test 2 | ||
December 4 | Spectral density, White Noise | |
December 6 | Linear Systems, Gauss-Markov, Karhunen-Loewe |
[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 6, 2002 | handed out Sept 13 [ps] [pdf] [tex] |
Problem Set 2 [ps] [pdf] [tex] | Sept 13, 2002 | handed out Sept 20 [ps] [pdf] [tex] |
Problem Set 3 [ps] [pdf] [tex] | Sept 20, 2002 | handed out Sept 27 [ps] [pdf] [tex] |
Problem Set 4 [ps] [pdf] [tex] | Sept 27, 2002 | handed out Sept 27 [ps] [pdf] [tex] |
Problem Set 5 [ps] [pdf] [tex] | Oct 11, 2002 | handed out Oct 18 [ps] [pdf] [tex] |
Problem Set 6 [ps] [pdf] [tex] | Oct 18, 2002 | handed out Oct 25 [ps] [pdf] [tex] |
Problem Set 7 [ps] [pdf] [tex] | Oct 25, 2002 | handed out Oct 30 [ps] [pdf] [tex] |
Problem Set 8 [ps] [pdf] [tex] | Oct 30, 2002 | handed out Oct 30 [ps] [pdf] [tex] |
Problem Set 8b [ps] [pdf] [tex] | not mandatory | handed out Oct 30 with problem set |
Problem Set 9a [ps] [pdf] [tex] | Nov 18, 2002 | handed out Nov 22 [ps] [pdf] [tex] |
Problem Set 10 [ps] [pdf] [tex] | Nov 27, 2002 | handed out Nov 27 [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) | Mo, Sept 30, 9:20-9:50 am | In class, 30 min, (open: only two hand-written pages ) |
Test 1 (30%) | Handed out: Mid October. | Take home, 3 hours, (open notes) |
Test 2 (30%) | Handed out: Late November. Due Dec 6 | Take home, 3 1/2 hours (open books) |