Rice University

**Instructor**

Dr. Rudolf Riedi

Duncan Hall 2025, 527 8750 x 3020,

Office Hours: Wednesday 2-3 pm, or by appointment

Ramesh Neelamani

Duncan Hall 2121, 527 8750 x 3230

Office Hours: Monday 2-3 pm, or by appointment

Tarik Muharemovic

Duncan Hall 2045, 527 8750 x 2371

Office Hours: Friday 9 - 10 am, or by appointment

**Time and Place**

TTH 10:50 - 12:05, Duncan Hall 1042

Further suggested readingH. Stark and J. Woods, `Probability, Random Processes, and Estimation Theory for Engineers'

- 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

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.

Covered material | Reading: Stark&Woods (1986) | |

August 31 | Orientation, history | |

September 2 | Probability space | pp 1-10 |

September 7 | Conditional Probability | pp 11-12, 15-17 |

September 9 | Bayes, Independence | (Binomial law:) pp 18-25 |

September 14 | Random variables, CDF, pdf | pp 37-51, (69-80) |

September 16 | Expectation, variance | pp 111-116 |

September 21 | Joint distributions | pp 62-67 |

September 23 | Functions of random variables | pp 73-87 |

Up to here: Material for Quiz | ||

September 28 | Conditional expectation, discrete | |

September 30 | Cond expect, continuous | pp 67-73, 117-123 |

October 5 | Cond expect=projection | pp 380-392 |

October 7 | Characteristic function | pp 139-146 |

October 12 | Multivariate Gaussian | pp 156-158, 170-173 |

October 14 | Covariance, Inequalities | pp 132-135 |

October 19 | Fall break | |

October 21 | Convergence (as, ms, ip, D) | pp 245-253 |

October 26 | ...and relations. Martingales | pp 254-256 |

October 28 | Limit theorems (MCT, LLN) | pp 135, 253, 257 |

November 2 | CLT, LDP, finite dimens. distr. | pp 143-146, 264-266 |

November 4 | stationarity, Renewals | pp 285-290 |

November 9 | Poisson Process | pp 267-273 |

November 11 | Wiener, Markov Processes | pp 273-281 |

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

November 16 | Spectral density | pp 337-342 |

November 18 | Mean square calculus | pp 296-307 |

November 23 | M.S. deriv, integral | pp 308-310 |

November 30 | Linear systems, Gauss-Markov | pp 287f,345f,280f |

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

December 2 | White Noise, KL | pp 343f |

December 7 | KL | pp 322-326 |

**Homework**
(Access restricted: graders only)

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

Problem Set 1 | Sept 14, 1999 | Set 1 |

Problem Set 2 | Sept 21, 1999 | Set 2 |

Problem Set 3 | Sept 28, 1999 | Set 3 |

Problem Set 4 | Oct 12, 1999 | Set 4 |

Problem Set 5 | Oct 21, 1999 | handed out in hard copy |

Problem Set 6 | Oct 26, 1999 | Set 6 |

Problem Set 7 | Nov 2, 1999 | handed out in hard copy |

Problem Set 8 | Nov 9, 1999 | Set 8 |

Problem Set 9 | Nov 16, 1999 | handed out in hard copy |

Problem Set 10 | Dec 2, 1999 | Set 10 |

Quiz (15% towards the grade) | Friday, October 1, 1999 | 4-4:45 pm, Abercrombie A 126 |

Midterm (30%) | Friday, Nov 19, 1999 | 2:50-6 pm, A 126 (open notes) |

Last Test (30%) | due: December 10, 1999 | take home, 7 days, 3 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 30, 1999.