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.*

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

**Instructor**

Dr. Rudolf Riedi

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.

- E. Wong and B. Hajek, `Stochastic Processes in Engineering Systems'

- A. Papoulis, `Probability, Random Variables, and Stochastic Processes'
- W. Davenport, `Probability and Random Processes'
- W. Feller, `An Introduction to Probability Theory and Its Applications'
- P. Billingsley, `Probability and Measure'

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) |

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.

May 17, 2001.