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.

Instructor

Dr. Rudolf Riedi
Duncan Hall 2082, 713 / 348 3020,
Office Hours: Tu 1:30-3:00, W 2:30-3:30pm
    or by appointment
Graders

       Deborah L. Goldwasser
       Hongxiao Zhu, aka "Hong"

Topics 

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]

Textbook

  • 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]

    Grading

    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]

     

    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]

    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.  Dr. Rudolf Riedi