Applied Probability

STAT 331, Fall 2004

Rice University

This course covers the basic concepts of Probability Theory and Statistics.
Targeted at undergraduate students it balances motivation, rigor and application of the relevant concepts through examples and homework. The course covers elementary concepts from probability theory and statistics such as the basic rules of probability, random variables, distributions, expected values, independence, correlations and estimation. Simple models (such as the Binomial and the Poisson models) are applied to real world problems in engineering and other fields.

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

Announcement  (Nov 23)

    The last week of classes is used for REVIEW sessions.

Time and Place
        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)

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


  • J. 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).
    Further suggested reading Standard references on Probability Theory
    [Outline] [Textbooks] [Grading] [Reading assignment] [Homework problems and solutions] [Tests]


    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
    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.
    October 12

    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
    October 26
    Sample averages and their distribution in the limit
    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

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

    (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]


    Late Homework Policy

    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 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".

    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.  Dr. Rudolf Riedi