Rice University

*This course covers the basic concepts of probability theory
and random processes*.

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

**Instructor**

Dr. Rudolf Riedi

Duncan Hall 2082, 713 / 348 3020,

Office Hours: M 3-4, Tu 4-5pm or by appointment

Rahul Chawathe

Alireza Keshavarz-Haddad

Monday 11:00-12:00, Wednesday 8:45 - 10:00 am, when Monday class cancelled : Friday 11:00-12:00

AL (Abercrombie Lab) 126

**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 27 | Orientation, history | |

August 29 | Probability space: basics | Review combinatorics: 24-31 |

September 3 | Probability space: discrete, continuous | 1-24 |

September 5 | Random variable, CDF, pdf | 58-68 |

September 10 | Conditional Probability, Bayes, Independence | 68-80 |

September 12 | Functions of one r.v., expectation | 116-134, 169-175 |

September 15 | Moments, Independent experiments | pp 192-196, 32-44 |

September 17 | Joint distributions, Marginals, Independent r.v. | pp 88-99 |

Up to here: Material for Quiz | ||

September 22 | Functions of two r.v., Sums and Products | pp 134-152 |

September 24 | Covariance, Stieltjes integral | |

September 26 | QUIZ | |

September 29 | NO CLASS, moved to Oct 3 | |

October 1 | generalized pdf (Dirac), conditional CDF | 75-80, 80-88 |

October 3 | conditional pdf, E[Y|X]: rules | 103-108 |

October 6 | E[Y|X]: several variables | 183-192 |

October 8 | MMSE, E[Y|X] as a projection, Gaussian estimation | 552-561 |

October 13 | RECESS, moved to Oct 17 | |

October 15 | Characteristic function | 216-225 |

October 17 | Joint char fct, joint Gaussian | 277- 280, 281 (also: 269-277) |

October 20 | Inequalities, Convergence of functions | pp 205-210, 375-376 |

October 22 | Convergence of random variables | pp 376-382 |

October 27 | Limit theorems | pp 383-387, 225-230, 214-216 |

October 29 | Limit theorems | |

Up to here: Material for TEST 1 | ||

November 5 | Random Processes: Basics | pp 401-407 |

November 7 | Consistency, Stationarity | |

November 12 | Renewal Processes: Basics | pp 408-416 |

November 14 | Poisson Process | |

November 19 | Consistency: Gaussian Processes | pp 418-421 |

November 21 | Consistency: Markov (Chapman-Kolmogorov) | pp 421-430 |

November 24 | Spectral density | 348-354 |

November 26 | Cross-correlation and -spectrum, Mean square continuity | 348-354, pp 487-490 |

November 28 | Thanksgiving | |

From Test 1 to here: Material for Test 2 | ||

December 1 | Mean square calculus | pp 487-497 |

December 3 | More of Spectral density, White Noise, 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 10, 2003 | [ps] [pdf] [tex] |

Problem Set 2 [ps] [pdf] [tex] | Sept 17, 2003 | [ps] [pdf] [tex] |

Problem Set 3 [ps] [pdf] [tex] | Sept 24, 2003 | [ps] [pdf] [tex] |

Problem Set 4 [ps] [pdf] [tex] | Oct 8, 2003 | [ps] [pdf] [tex] |

Problem Set 5 [ps] [pdf] [tex] | Oct 15, 2003 | [ps] [pdf] [tex] |

Problem Set 6 [ps] [pdf] [tex] | Oct 22, 2003 | [ps] [pdf] [tex] |

Problem Set 7 [ps] [pdf] [tex] | Oct 29, 2003 | [ps] [pdf] [tex] |

Problem Set 8 [ps] [pdf] [tex] | Nov 21, 2003 | [ps] [pdf] [tex] |

Problem Set 9 [ps] [pdf] [tex] | for practice only, not graded | handed out with problem set
[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 instructors's office door, 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) | Sept 26, 11:00-11:40, AL 126. | In class, 30 min, (open: only two hand-written pages ) |

Test 1 (30%) | Handed out: Mid October. To be scheduled | Take home, 3 hours, (open notes) |

Test 2 (30%) | Handed out: Late November. To be scheduled | 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.

August 1, 2003.