Clark University
                                        Math 217/Econ 360, Probability and Statistics
Fall 2014
Prof. D. Joyce, BP 322, 793-7421
Department of Mathematics and Computer Science
Clark University

Pierre-Simon Laplace (1749–1827)
   
Portraint of Pierre Simon Laplace
   
click for source Portrait of Laplace at the Palace of Versailles
Date 1842, posthumous portrait by Sophie Feytaud


Please bookmark this page, http://aleph0.clarku.edu/~djoyce/ma217/, so you can readily access it.

Course information

Class notes, quizzes, tests, homework assignments

The dates for the discussion topics and the assignments are tentative. They will change as the course progresses.

    [to be filled in as the course progresses]

  1. Monday, Aug 25. Welcome and introduction to the class
    Intro to probability via discrete uniform probabilities. Symmetry. Frequency.
    Simulations and random walks

  2. Wednesday, Aug 27.
    Background on sets. Unions, intersections, complements, distributivity, DeMorgan's laws. Product, power sets. Countable and uncountable infinities.
    Combinatorics. Principle of inclusion and exclusion, multiplicative principle, permutations, factorials and Sterling's approximation
    Permutation generating applet
    Assignment 1 due next Wednesday.

  3. Friday, Aug 29. Binomial coefficients.
    Combinations, Pascal's triangle, multinomial coefficients, stars & bars, combinatorial proofs
    The BinomialPlot and GaltonBoard applets

    Monday, Sep 1. Labor Day. No classes

  4. Wednesday, Sep 3. Axioms for probability distributions.
    Probability mass mass functions for discrete distributions, density functions for continuous distributions. Cumulative distribution functions. Sample spaces, axioms, and properties.
    Assignment 1 due. Answers
    Assignment 2 due next Wednesday.

  5. Friday, Sep 5. Uniform finite probabilities
    Odds. Repeated trials. Sampling with replacement. The birthday problem.
    The Birthday applet

  6. Monday, Sep 8. Proofs of properties of probability distributions from the axioms.
    Conditional probability. Xox.

  7. Wednesday, Sep 10.
    More on conditional probability: definition of conditional probability, the multiplication rule
    Assignment 2 due. Answers.
    Assignment 3 due next Wednesday.

  8. Friday, Sep 12. Bayes' formula. Examples, tree diagrams

  9. Monday, Sep 15.
    Independent events. Definition, product spaces, independence of more than two events, joint random variables, random samples, i.i.d. random variables
    Bertrand's box paradox

  10. Wednesday, Sep 17.
    The Bernoulli process. Sampling with replacement. Binomial distribution, geometric distribution, negative binomial distribution, hypergeometric distribution. Sampling without replacement
    Assignment 3 due.

  11. Friday, Sep 19.
    Discrete random variables. Probability mass functions, cumulative distribution functions. Various graphs and charts

  12. Monday, Sep 22.

More notes Other information.


This page is located on the web at

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

David E. Joyce