This course page is obsolete.  I'll prepare a new page next time I teach the course.

Course information

• General description. An introduction to probability theory and mathematical statistics that emphasizes the probabilistic foundations required to understand probability models and statistical methods. Topics covered will include the probability axioms, basic combinatorics, discrete and continuous random variables, probability distributions, mathematical expectation, common families of probability distributions, and the central limit theorem.
  This course is cross-listed as Econ 260 and as Econ 360.
  See also Clark's Academic Catalog
• Prerequisites. One year of college calculus (Math 121 or 125).
• Course goals.
  • To provide students with a good understanding of the theory of probability, both discrete and continuous, including some combinatorics, a variety of useful distributions, expectation and variance, analysis of sample statistics, and central limit theorems, as described in the syllabus.
  • To help students develop the ability to solve problems using probability.
  • To introduce students to some of the basic methods of statistics and prepare them for further study in statistics.
  • To develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to basic probability.
  • To make connections between probability and other branches of mathematics, and to see some of the history of probability.
• Syllabus
• Textbook. Charles M. Grinstead and J. Laurie Snell's textbook Introduction to Probability, published by the American Mathematical Society, 1997. It is also on-line at http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html ..
• Course Hours. MWF 12:00-12:50. BP 326.
• Office hours. Semester schedule
• Assignments & tests. There will be numerous short homework assignments, mostly from the text, occasional quizzes, two tests during the semester, and a two-hour final exam during finals week.
• Course grade. The course grade will be determined as follows: 2/9 assignments and quizzes, 2/9 each of the two midterms, and 1/3 for the final exam.

Class notes, quizzes, tests, homework assignments

• Friday, Dec 7. Notes. A proof of the central limit theorem.
• Wednesday, Dec 5. Notes. Properties of the moment generating functions, and examples from continuous distributions.
• Monday, Dec 3. Notes. Standardized sums. Examples illustrating the central limit theorem. Confidence intervals.
• Friday, Nov 30. Notes. The chi-squared distriubution, sample variance for a normal distribution, introduction to the central limit theorem.
  Exercises from 7.1: 3, 6; and from 7.2: 2a, 3a, 5a.
• Wednesday, Nov 28. Notes. The Chebyshev inequality. Sample statistics and estimators, sample variance.
• Monday, Nov 26. Notes. The law of large numbers.
• Monday, Nov 19. Notes. The distribution of sample sums. Convolution.
  Exercises from section 6.3: 2, 6ab, 17, 18.
• Friday, Nov 16. Notes. The mean and variance of an exponential distribution. The lack of a mean and variance for a Cauchy distribution.
  Exercises from section 6.2: 1, 2, 7, 11, 12, 23.
• Wednesday, Nov 14. Notes. Expectation, mean, variance for continuous distributions.
• Monday, Nov 12. Second test on sections 4.1--4.2, 5.1--5.2, and 6.1.
• Friday, Nov 9. Review.
• Wednesday, Nov 7.
• Monday, Nov 5. Notes. Variance and standard deviation for discrete random variables.
  Exercises from section 6.1: 7, 8, 16, 17.
• Friday, Nov 2. Notes. Conditional expectation for discrete random variables.
  Exercises from section 6.1: 1-6, 18.
• Wednesday, Oct 31. More on expected value.
  Exercises from section 5.2: 22ac, 23, 25, 27.
• Monday, Oct 29. Notes.
  Exercises from section 5.2: 1, 2, 7, 12a, 13a, 16.
• Friday, Oct 26. Notes. The normal distribution. Introduction to expected value.
  Exercises from section 5.1: 7, 9, 16, 18, 25.
• Wednesday, Oct 24. Notes. Gamma and Beta functions and distributions.
  Quiz on chapter 4.
• Monday, Oct 22. Notes. Functions of random variables. The Cauchy distribution.
  Exercises from section 5.1: 1, 2, 4, 8.
• Friday, Oct 19. Notes. The Poisson process.
• Wednesday, Oct 17. Notes. Introduction to families of distributions.
• Monday, Oct 15. Notes. More on joint density functions.
  Exercises from section 4.2: 1, 4, 5, 6abc, 8.
• Friday, Oct 12. Conditional density functions, joint distributions and density functions.
  Exercises from section 4.1: 35, 39, 51.
• Wednesday, Oct 10. Notes. Introduction to continuous conditional probability.
  Exercises from section 4.1: 14, 16, 17, 22, 27.
• Friday, Oct 5. Notes. Examples for Bayes' formula.
  Exercises from section 4.1: 1-9
• Wednesday, Oct 3. Return tests, discuss product spaces, joint random variables, independence.
• Monday, Oct 1. First test Answers.
• Friday, Sep 28. Notes. Review.
• Wednesday, Sep 26. Notes. Conditional probability.
• Monday, Sep 24. Notes. The problem of points, hypothesis testing.
  Exercises from section 3.2.
• Friday, Sep 21. Notes. Binomial distribution, binomial theorem.
• Wednesday, Sep 19. Notes. Pascal's triangle, Bernoulli trials, Bernoulli process.
  Exercises from section 3.1
• Monday, Sep 17. Notes. Combinations, binomial coefficients.
  More exercises from section 2.2
• Friday, Sep 14. Notes. Intro to the normal distribution, intro to combinatorics, multiplicative principle, permutations both full and partial.
  Some exercises from section 2.2
• Wednesday, Sep 12. Notes. More examples of continuous random variables, introduction to the Poisson process.
  Quiz.
• Monday, Sep 10. Notes. Density functions for continuous random variables.
  Some more exercises from section 1.2
• Friday, Sep 7. Notes. Introduction to continuous probability.
• Wednesday, Sep 5. Notes. Uniform finite distributions, odds.
  Some exercises from section 1.2 introduction to continuous probability.
• Friday, Aug 31. Notes. Axioms for probability.
  Exercises from section 1.1
• Wednesday, Aug 29. Notes. Distribution functions, random walks.
  Java applets at http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/bookapplets/index.html
• Monday, Aug 27. Welcome. Notes.

Other information.

• Common probability distributions, Table of distributions
• Last year's midterms and final
  • First midterm.
  • Second midterm.
  • Final examination.
• Web sites
• Humor in mathematics

This page is located on the web at

http://aleph0.clarku.edu/~djoyce/ma217/

David E. Joyce