STAT 461/561 (MATH 441) PROBABILITY

Department of Mathematics and Statistics, UNM

Fall Semester 2010 Webpage: http://www.math.unm.edu/~ghuerta/stat561/course.html

INSTRUCTOR

Dr. Gabriel Huerta
email: ghuerta "at" stat.unm.edu
Office: 443 Humanities Bldg.
Class Time: T,R 12:30-13:45.
Classroom: 229 Dane Smith Hall
Office Hours: T,R 14:00-15:15 at the Dane Smith Hall Atrium ( or by appointment).

DESCRIPTION

This course is about mathematical models for random experiments, random variables, expectation. The common discrete and continuous distributions with application. Joint distributions, conditional probability and expectation, independence. Laws of large numbers and the central limit theorem. Moment generating functions.

PREREQUISITES

Math 264: Calculus III.

TEXTBOOK

  • Casella, G. y Berger, R.L. (2001) Statistical Inference. 2th ed. Duxbury Press (required).

    We will be covering most of the material in Chapters 1-4 from this book.

  • Ross, S. (2010) A First Course in Probability 8th ed. Prentice Hall (recommended).

    This book will be used to supplement the material in Casella and Berger for class examples or exercises.

    • TOPICS

  • Probability theory, random variables, density and distribution functions.
  • Functions of random variables, expected values, moments and moment generating functions.
  • Discrete and continuous distributions. Families of Distributions. Inequalities.
  • Joint, marginal and conditional distributions. Covariance and Correlation.
  • Random samples. Functions of random samples (sums, means)
  • Ex. 3.5 and 3.7 R code
    SUGGESTED LIST OF EXERCISES FROM Casella and Berger (to be updated regularly)

    ** I see this as a minimal list of exercises you should try to learn the class material. The more exercises you work with from this list and beyond, the better prepared you will be for tests.

  • Chapter 1: 1.1, 1.3, 1.4, 1.9, 1.5,1.7, 1.11,1.16, 1.22, 1.24, 1.33, 1.36, 1.38, 1.47, 1.51.
  • Chapter 2: 2.2, 2.6, 2.9, 2.12, 2.20, 2.22, 2.25, 2.30, 2.32, 2.33
  • Chapter 3: 3.1, 3.3, 3.4, 3.8(b), 3.9, 3.13, 3.20, 3.21, 3.23, 3.24
  • Chapter 4: 4.5, 4.9, 4.14, 4.15, 4.17, 4.24
  • Test No. 2. on November 18. Will cover material from Chapter 2: secs. 2.2 and 2.3. Material form Chapter 3: secs. 3.1,3.2,3.4 and 3.6.1 and perhaps something on Chapter 4, secs. 4.1 and 4.2
  • Take home final Exam . Due on Tuesday, December 14 at noon HUM 443.
    GRADING

    The grade will be based exclusively in two midterm exams and a take-home final exam. Each midterm is worth 30 % of the course grade. The final is worth 40%. The first midterm exam will be on Thursday, September 23. Suggested exercises from the textbook will be assigned regularly but they will NOT be graded. I will post the list of exercises in the class webpage. Solutions for selected problems will be discussed in class or provided through this page. I also encourage you to work the exercises in small groups. It is very important to make and effort to go beyond class lectures and work through the exercises (suggested or more) to understand the class material.

    MAKE-UP POLICY

    There are no make up exams. Only in case of an emergency that can be throughly documented with a medical or police report, I will consider rescheduling an exam at an alternative date.

    UNM POLICY

    Qualified students with disabilities needing appropriate academic adjustments should contact me to ensure that they are met in a timely manner.