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 46pm and W 1012am (DH 2025), or by appointment
Bhaskar Nallapureddy
Duncan Hall DH1040, 713 / 348 3579,
Office Hours: MW 4:30pm5:30pm, or by appointment
Mohammed Ahamed KhanTime and Place of Classes
Duncan Hall DH2113, 713 / 348 2776,
Office Hours: TTh 10:3011:30am, 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 115, Combinatorics: 2431 
September 4  SigmaAlgebra, Borel sets, continuous spaces  read pp 1624 
September 6  Bayes, Independence, Random variables  pp 5868 
September 9 (instead Wed)  CDF, density (pdf), functions of one r.v.  pp 6880, 129 
September 13  HW 1, expectation, E[g(X)]  pp 116134, 169175 
September 18  Moments, Independent experiments  pp 192196, 3244 
September 20  Joint distributions, Marginals, Independent r.v.  pp 8899 
Up to here: Material for Quiz  
September 25  Functions of two r.v., Sums and Products, Covariance  pp 134152 
September 27  Stieltjes integral, generalized density (Dirac)  
October 2  Conditional density and expectation E[YX]  pp 8088, 103108 
October 4  E[YX]: rules, several variables  pp 183192 
October 9  Characteristic function, Cumulants  pp 216225 
October 11  Multivariate Distributions, Covariance  pp 269277 
October 16  Jointly Gaussian: distribution and estimation  pp 269277, 556561 
October 18  Convergence of functions and random variables  pp 375379 
October 23  Inequalities, Comparison of Convergence  pp 205210, 375379 
October 25  Comparing convergence, Martingales  pp 225230, 383387 
Monday October 28  Limit theorems (Martingales and LLN)  pp 383387, 225230, 214216 
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 401407 
November 8  Autocorrelation, Stationarity  pp 
Monday November 11 (instead 13)  Renewal processes, Poisson  pp 408414 
November 13  NO CLASS 

November 15  NO CLASS  
Monday November 18 (instead 15)  Poisson properties  pp 408416 
November 20  Consistency: Gaussian Processes, Markov  pp 418421, 421430 
November 22  ChapmanKolmogorov,  pp 429430 
Monday November 25 (Thanksgiving)  Spectral density  348354 
November 27  Mean square calculus  pp 487497 
November 29  Thanksgiving  
From Test 1 to here: Material for Test 2  
December 4  Spectral density, White Noise  
December 6  Linear Systems, GaussMarkov, KarhunenLoewe 
[Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]
Homework
(texsource 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, 9:209:50 am  In class, 30 min, (open: only two handwritten 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) 