Rice University

**Instructor**

Dr. Rudolf Riedi

Duncan Hall 2025, 713 / 348 3020,

Office Hours: Tuesday 1-2 pm and 5-6 pm, or by appointment

Ramesh Neelamani

Duncan Hall 2121, 713 / 348 3230

Office Hours: Monday 1:45-2:45, 5-6 pm, or by appointment

Vinay Keshavan Bharadwaj

Duncan Hall 2047, 713 / 348 2471

Office Hours: Thursday 1-3 pm, or by appointment

**Time and Place**

Wednesday Friday 9:00 - 10:15 am, AL (Abercrombie Lab) 126

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

15% QUIZ

30% Midterm EXAM

30% Last EXAM

15% Homework

10% Notes and participation in class

This part will be updated during the semester helping you to identify the material covered in class and where to find further reading.

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 |

Covered material | Reading: Stark&Woods (1994) | |

August 29 | Orientation, history | |

August 30 | Probability space | pp 1-12 |

September 1 | Borel sets | read ahead: pp 21-28 |

September 6 | Conditional Prob., Bayes, Independence | pp 13-21 |

September 8 | Bernoulli trials, Random variables | pp 28-36, 52-56 |

September 13 | CDF, pdf, functions of one r.v. | pp 56-60, 66-74, 106-122 |

September 15 | Expectation, variance | pp 160-165, 178-180 |

September 20 | Expect. (examples), Joint distributions | pp 74-87 |

September 22 | Joint distributions, Marginals, Independent r.v. | pp 88-92 |

September 25 | Functions of two r.v., Sums and Products | pp 122--140 |

Up to here: Material for Quiz | ||

September 29 | Conditional distribution, discrete | pp 74-81 |

October 4 | Discussion on Quiz, Conditional expectation | pp 170-178 |

October 6 | Cond expect, continuous | pp 170-178 |

October 11 | Correlation, jointly Gaussian r.v. | pp 182-193 |

October 13 | Estimation of r.v. | pp 296-303 |

Fallbreak | ||

October 18 | Characteristic function | pp 204-213, 258-261 |

October 20 | Multivariate Gaussian, Covariance, Inequalities | pp 261-263, 248-258, 194-198 |

October 25 | Conv. of functions (pointwise, uniform ,L2) and r.v. (as, ms) | pp 348-353 |

October 27 | Convergence of r.v. (as, ms, ip, D) | pp 348-357 |

November 1 | Limit theorems (LLN, CLT) | pp 357-362, 213-218 |

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

November 3 | Random Processes, basics | pp 318-326, 371-376 |

November 6 | R.P. examples, Auto-correlation, Stationarity | pp 326-336 |

November 8 | Renewal processes, Poisson | pp 376-386 |

November 15 | Poisson, Markov, Gaussian Processes | pp 377-386, 391-396 |

November 17 | Consistency, Brownian motion | pp 330-331, 386-391, 396-399 |

November 22 | Colored noise, Gauss Markov, Spectral density | 391-393, 395-399 |

November 24 | Thanksgiving | |

November 29 | (Cross) Spectral density, mean square continuity | pp 465-472, 419-422 |

December 1 | Mean square calculus, White Noise | pp 422-430 |

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

December 6 | Linear Systems with random input | pp 399-404, 433-437 |

December 8 | KL | pp 450-457 |

**Homework**
(tex-source for graders only)

Homework sheet | Due date (in class) | Solutions |

Problem Set 1 [tex] | Sept 13, 2000 | handed out Sept 20 Set 1 [tex] |

Problem Set 2 [tex] | Sept 20, 2000 | handed out Sept 25 Set 2 [tex] |

Problem Set 3 [tex] | Sept 27, 2000 | handed out Sept 29 Set 3 [tex] |

Problem Set 4 [tex] | Oct 13, 2000 | handed out Oct 13 Set 4 [tex] |

Problem Set 5 [tex] | Oct 120, 2000 | handed out Oct 27 Set 5 [tex] |

Problem Set 6 [tex] | Oct 27, 2000 | handed out Nov 1 Set 6 [tex] |

Problem Set 7 [tex] | Nov 3, 2000 | handed out Nov 10: Neelsh |

Problem Set 8 [tex] | Nov 8, 2000 | handed out Nov 10 Set 8 [tex] |

Problem Set 9 [tex] | Nov 29, 2000 | handed out Dec 5 Set 9 [tex] |

Problem Set 10 [tex] | Dec 1, 2000 | handed out Dec 1 Set 10 [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.

Quiz (15% towards the grade) | Monday, October 2nd, 9:00 - 9:45 am | (open: only two personal pages ) |

Midterm (30%) | Handed out Nov 10 (Duncan 2121), due Nov 15 midnight. | take home, 3 hours, open notes |

Last Test (30%) | Handed out Dec 1, due Dec 8 noon | take home, 7 days, 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 7, 2000.