Rice University

*This course covers the basic concepts of Probability
Theory
and Statistics*.

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

Announcement (Nov 23)

The last
week of classes is used for REVIEW sessions.

According to the official Rice web page.

Tuesday Thursday 9:25-10:40 in Duncan Hall 1064.

Dr. Rudolf Riedi

Duncan Hall 2082, 713 / 348 3020,

Office Hours: Tu 1:30-3:00, W 2:30-3:30pm

or by appointment

Deborah L. Goldwasser

Hongxiao Zhu, aka "Hong"

Basic Probability,
axioms of probability, Bayes rule, Independent events

Random variables, distributions, expected values, Bernoulli Trials

Bivariate variables, multivariate distributions, independent r.v., correlations

Generating functions, characteristic function

Midterm Homework (open-discussion)

Continuous random variables

Limits and convergence, Law of Large Numbers, Central Limit Theorem

Simple models with applications, Gaussian, Rayleigh, Poisson

Midterm EXAM (open-notes)

Estimation, mean, variance

Linear regression, model fitting

Reliability, Poisson model

Second EXAM (open-books)

Random variables, distributions, expected values, Bernoulli Trials

Bivariate variables, multivariate distributions, independent r.v., correlations

Generating functions, characteristic function

Midterm Homework (open-discussion)

Continuous random variables

Limits and convergence, Law of Large Numbers, Central Limit Theorem

Simple models with applications, Gaussian, Rayleigh, Poisson

Midterm EXAM (open-notes)

Estimation, mean, variance

Linear regression, model fitting

Reliability, Poisson model

Second EXAM (open-books)

Further suggested readingJ. R. Cogdell`Modeling Random Systems"

The course will closely follow this book; it is available at the campus bookstore.

One copy of the book is "on reserve" at Fondren (2 hours at a time).

**H. 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'

40% Homework (double points at midterm: HW5)

30% Midterm EXAM (late October)

30% Last EXAM (late November)

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

**Classes** / Reading

Past classes and reading assignment will be posted here.

Topics covered

reading [exercises]

August 24

Orientation, Introduction to Probability

Bernstein: "Against the Goods"

August 26

I. Set Theory, relative frequencies

Cogdell pp 1-26 [56-58]

August 31

Axioms of Probability, Conditional Probabilities, Independence

pp 26-37 [59-63]

September 2

Bayes, Total Probabiilty, Equally likely outcomes, Poisson, Geometric

pp 38-55, 92-94 [64-84]

September 7

Bernoulli trials, Binomial, Geometric and Pascal distributions

pp 85-98 [142-151]

September 9

II. Random variables pp 99-114 [152-158]

September 14

Joint Distr., Marginals, Independence

pp 114-122 [159-160]

September 16

Expectation, mean, variance, total probability

pp 123-135 [160-165]

September 21

Joint Expectation, Covariance, Rules ditto

September 23 Conditional Expectation, Characteristic Function

ditto

September 28

III. Continuous random variables: intro, CDF

175-177, 186-190

September 30

probabilty density function, pdf conditioned on an event 178-185,191-199

October 5

mixed CDF, joint and marginal pdf, independence

200-209, 216-221

October 7

conditional pdf and moments for continuous r.v.

210-215

October 12

Recess

October 14

Characteristic function for continuous r.v.

Lecture notes

October 19

IV. Convergence and limits: Bernoulli and Pascal, geometric and exponential 216-225 October 21

Gaussian distribution, Raleigh

235-247,256-259

October 26

Sample averages and their distribution in the limit

226-236,248-255

October 28

Central Limit Theorem (interpretation, applications)

November 2

Convergence of r.v. and the Law of Large Numbers

November 4+9

V. Statistics

Bias, consistency, spot and range, MLE

Estimating the mean and variance

Chapter 4.1

November 11

Review basic estimation

Chapter 4.1

November 16

Linear regression

Chapter 4.2

November 18

Fitting of CDF to data, bivariate Gaussian

Chapter 4.2

November 23

Regression and Correlation. Hypothesis Testing

Chapter 4.3

Nov 25

Thanks Giviing

November 30

Poisson Model. Review Statistics

December 2

Review

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

**Homework**

(tex-source and solutions restricted to Rice University)

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

Problem Set 1 [pdf] [ps] [tex] | September 9, 2004 |
Solution 1 [pdf] [ps] [tex] |

Problem Set 2 [pdf] [ps] [tex] | September 16, 2004 | Solution 2 [pdf] [ps] [tex] |

Problem Set 3 [pdf] [ps] [tex] | September 23, 2004 | Solution 3 [pdf] [ps] [tex] |

Problem Set 4 [pdf] [ps] [tex] | September 30, 2004 | Solution 4 [pdf] [ps] [tex] |

Midterm HW 5 [pdf] [ps] [tex] | October 14 |
Solution 5 [pdf] [ps] [tex] |

Problem Set 6 [pdf] [ps] [tex] | October 21 |
Solution 6 [pdf] [ps] [tex] |

Problem Set 7 [pdf] [ps] [tex] | October 28 |
Solution 7 [pdf] [ps] [tex] |

Problem Set 8 [pdf] [ps] [tex] | November 18 |
Solution 8 [pdf] [ps] [tex] |

Problem Set 9 [pdf] [ps] [tex] | November 23 |
Solution 9 [pdf] [ps] [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]

Midterm Homework (double points,
review) |
Due: Oct 14 |
usual HW rules |

Test 1 (30%) |
Due: Nov 9, midnight. Use an envelop to hand in. Include frontpage. |
Take home, 210 minutes, (open notes) |

Test 2 (30%) | Due: Dec 3, 23:59. Use an envelop to hand in. Include frontpage. | Take home, 3 hours (open books) |

Honor System

Homework:

Homework are "open-discussion". This means the following:

Collaboration for homework is encouraged. Any source of information is admissible. However, each student hands in her/his own homework which expresses his/her own understanding of the solution. Simple copying from others does not qualify as "collaboration".

Tests:

The term "open notes" means that look-up in any self-compiled hand-written source of knowledge is permitted.

The term "open books" means that look-up in any passive source of knowledge is permitted.

No help of any kind is allowed. For instance, no communication is admissible which involves any intelligent entity ---human or artifical--- or any active source which is able to respond to questions .

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 21, 2004.