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,, 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. Answers.
    Assignment 4 due next Wednesday.

  11. Friday, Sep 19.
    Discrete random variables. Probability mass functions, cumulative distribution functions. Various graphs and charts
    Expectation for discrete random variables. Definition, expectation for the binomial and geometric distributions. St. Petersburg paradox.

  12. Monday, Sep 22.
    Select the date for the first test. It will cover chapter 1 through most of chapter 4.
    More on expectation. Properties of expectation.
    Variance for discrete random variables. Definition and properties.

  13. Wednesday, Sep 24.
    Variance of the binomial and geometric distributions.
    Assignment 4 due. Answers.
    Assignment 5 due next Wednesday.

  14. Friday, Sep 26.
    Continuous probability. Monte Carlo estimates. Introduction to the Poisson process and the normal distribution. Statement of the central limit theorem.

  15. Monday, Sep 29.
    Density functions. Density as the derivative of the c.d.f., and the c.d.f. as the integral of density.

  16. Wednesday, Oct 1.
    Assignment 5 due. Answers.

  17. Friday, Oct 3.
    Examples of continuous distributions, functions of random variables, the Cauchy distribution.

  18. Monday, Oct 6. Review for first test
    Sample first test

  19. Wednesday, Oct 8.
    First test. Covers chapter 1 through 4. Answers.

  20. Friday, Oct 10.
    The Poisson process. The Poisson, exponential, gamma, and beta distributions. Axioms for the Poisson process.

    Monday, Oct 13. Fall break. No classes.

  21. Wednesday, Oct 15.
    Expectation and variance for continuous random variables. Definitions and properties. Expectation and variance for uniform and continuous distributions. Lack of expectation and variance for the Cauchy distribution.
    Assignment 6 due next Wednesday.

  22. Friday, Oct 17. The normal distribution, table for the c.d.f. of the standard normal distribution, the normal approximation to the binomial distribution. DeMoivre's 1733 proof for the first instance of the Central Limit Theorem.

  23. Monday, Oct 20.
More notes Other information.

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David E. Joyce