UNIVERSIDAD NACIONAL DE COLOMBIAFACULTAD DE CIENCIAS

Departamento de EstadsticaSemester 01-2013

Course: Basic Theory of ProbabilityCode: 2020932-1Week hours:4Graduate Program: Specialization in StatisticsProfessor: Henry Mendoza Rivera.E-mail: hmendozar@unal.edu.co Skype:hmendozarLecture: Tuesday and Thursday 6:00 p.m.- 8:00 p.m. Building 405 room 209Office Hours: 9:00 AM-11:00 AM, Wednesdays and Fridays in Building 405 Office 333. Pleasesend an e-mail a day before to make your appointment.

Course Description and Purpose

Theory of Probability is considered to be a major component in statistic.There are two approaches to the study of probability theory. One approach is nonrigorous. The otherapproach is rigorous and use tools of measure theory. This course will use the minimal topics frommeasure theory. We will concern more on the basic theory of probability at graduate level. However,we will focus both on understanding and applications.This course deals with the basic theory of probability, and application of probabilistic models in examplecases and situations related to different fields such as engineering, computer science economy, education,finance among others. The course covers theory, application, and interpretation of probabilistic models.Emphasis in the course is on the mastery of concepts and theory, and development of critical analysisskills in understanding research using the covered basic theory of probability.

Chapters and Tentative Course Organization

Chapters

Chapter Title01 Probability02 Random Variables03 Moments and Generating functions04 Limit Theorems05 Special Distributions (discrete)06 Special Distributions (continuous)07 Sample Statistics

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Tentative Course Organization

Week Lecture Chapter Topic01 01 01 Introduction, Sets and Sigma algebras01 02 01 Probability Axioms02 03 01 Counting rules and examples02 04 01 Conditional probability and Independence, Bayes Theorem03 05 02 Random variables and distribution functions(univ., and mult.)03 06 02 Discrete (univ., and mult.)04 07 02 Absolutely continuous random variables (univ., and mult.)04 08 01 and lectures:5,6,7 Test 105 09 02 Distribution of functions of random variables (Discrete)05 10 02 Distribution of functions of random variables (continuous)06 11 02 Conditional distributions and independence06 12 03 Expectation and Moment07 13 03 Tchebychev Inequality, and Conditional expectation07 14 03 Multivariate moments, and Generating functions08 15 03 Order Statistics08 16 03 Characteristic function09 17 03 Multivariate Generating function09 18 02,03 Test 210 19 04 Modes of convergence10 20 04 Modes of convergence11 21 04 Law of large numbers, and Central limit Theorem11 22 05 Binomial an Negative Binomial Distribution12 23 05 Discrete Uniform, Poisson, and Hypergeometric Distribution12 24 05 Multinomial,Uniform and Gamma Distribution13 25 06 Beta,Dirichlet and Cauchy Distribution13 26 06 Multivariate normal including quadratic forms14 27 06 Sample Statistic, and Delta Method14 28 07 Asymptotically normal15 29 07 Chi-square, Student and F distribution, sample correlation15 30 Review16 31 All chapters Final Exam

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Textbook, and References

Textbook:

An Introduction to Probability and Statistics Vijay K. Rohatgi and A.K.Md.Ehsanes Saleh.2001, JohnWiley and Sons, Inc.

References in alphabetical order

Bartle, R.G. (1966). Elements of Integration. Second edition. John Wiley and Sons, Inc.

Blanco,C. L.,Arunachalam,V. and Dharmaraja, S. (2012) Introduction to Probability and StochasticProcesses with Applications.,John Wiley & sons.

Capinski,M & Zastawniak,T. (2001). Probability Through Problems.Springer-Verlag New York,Inc.

Feller,W. (1970) An introduction to Probability Theory and its Applications. John Wiley. Thirdedition.

Mathematical Statistics with Applications, 7th edition. (2008), by Wackerly, D., Mendenhall, W., andScheaffer, R.

Jacod, J. and Protter, P. (2003) Probability Essentials, 2nd ed. Springer-Verlag.

R Development Core Team, R: A language and environment for statistical computing, R Foundationfor Statistical.

Ross,S. (2010) A first course in Probability. Prentice Hall. 8th Edition.

Stewart, J. (2008). Multivariable Calculus: Early Transcendentals, Sixth Edition Thomson Learning,Inc

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Methodology

The course methodology will be based on activities such as lectures, discussions, homework.

Grading

Percentage Date ContentsTest 1 20 Week 4: Class 2 All covered topics la fechaTest 2 20 Week 9: Class 2 All covered topicsFinal Exam 30 Week 16: Class 1 All All topics covered on the semesterHomeworks 20 Monday after postedQuizzes 10

Important Remarks

1. Academic integrity:

For this course, you should work mostly independently on the homework. You may consult the instructoror other students while working on the homework, but you must acknowledge this help by making anote on your homework. Also, you must write your final solutions independently and may not copyhomework from other students or any other source.

2. Homework:

Homework assignments will be posted periodically on the course web page and will be due on Mondaysat 11:55 PM a week after homework posted. You have to turn in by log in the Learning ManagementSystem used by the university: http://www.campus.virtual.unal.edu.co. Then entering your email userand the corresponding password. You have to attached a .zip file with the .pdf and LaTeX files in theoption menu called Assignments. Late homework will not be accepted. Homework will count for 20percent of your course grade. Along with your individual homework, another feature of the course willbe team homework assignments. Each of the team problems will require considerable thought and acomplete, well-written solution. Your grade for each team homework assignment will be assigned to theteam as a whole, so everyone in your group will be responsible for each others learning of the material.

3. Quizzes:

There will be unannounced short (5-minutes) quizzes during class at random times throughout thesemester. Quizzes will usually be given near the end of class, but may be given at the beginning of classoccasionally. Your performance on these quizzes will count for 10 percent of your grade. Some quizzeswill be posted in the Learning Management System used by the university . None of these quizzesmay be made up.

3. Tests and Final Exam:

You can bring to the Final Exam and every Test your own double sided cheat sheet. The tests andFinal Exam must be submitted on white letter-size paper.

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4. Software:

LaTeX

To write in Latex you can download and install:

1. MikTeX, the LaTeX distribution is the core of the system. It contains the most important programsneeded for generation of DVI, Postscript and PDF, and all additional packages. Download fromhttp://www.miktex.org/2.9/setup (90 - 1000 MB)

2. The package Ghostscript http://downloads.ghostscript.com/public/gs905w32.exe (10 MB)

3. The package GSview http://pages.cs.wisc.edu/ ghost/gsview (3 MB)

4. The LaTeX editor package. You can use one of the following: Textudio, Texmaker, Lyx, Texniccenter

Statistical program R

Some homework will require calculations using the statistical program R. You can download it fromhttp://www.r-project.org/

5. Bonus Points:

Each academic activity for bonus points will give you at the most 100 points. One you complete 5 bonuspoints, you can change the total score on these bonus points by a grade quiz. That is, for example isyou get a total of 500 points and you have some Quiz gradet 200, you will ask the professor to changeit by 500. Then your new Quiz grade will be 500 instead of 200.Note: An academic activity for bonus points can be: Quiz corrections, test corrections, lecture classnotes, exercise class, or any assigned academic activity assigned by the professor. To be valid andparticipate for bonus points you have to send them by BlackBoard in the menu option called Bonusand attach on it the pdf and Latex file.

6. Internet Resources:

Most course information will be posted on BlackBoard or through e-mail. It is your responsibility tocheck these resources on a regular basis.

7. Study skills:

Useful videos about Study Skills

8. This Document:

This policy sheet is tentative and is subject to change. Any changes will be announced in class, throughe-mail, and on BlackBoard, and an updated version of the syllabus will be posted on BlackBoard orDropbox.

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