This exam will be given in class on Tuesday, May 5, 2009.

It will be a closed-book exam. You may use your own copy of the Table of Discrete Distributions (written on one side only). You may also use your 3"-by-5" note cards prepared for previous exams.

It will feature problems and questions on the following
TOPICS:

• Discrete random variables and their distributions
• Special discrete probability distributions
• Discrete probability distributions and their related summation formulas
  • Binomial theorem
  • Geometric series
  • (Newton's) binomial series
  • Vandermonde identity
  • Exponential series
• Mean/expected value
  • Techniques for calculating expected values
    • Look 'em up
    • Summation calculus
    • Probabilistic insight
    • Generating functions
  • Mean/expected value of a discrete random variable or distribution
  • Law of the Unconscious Statistician
  • Probability generating function
  • Moments
    • Ordinary moments, central moments, factorial moments, variance, standard deviation
    • Covariance, correlation (coefficient)
    • Moment generating function: not on the exam
  • Means, covariances, and variances of sums of r.v.s or linear combinations of r.v.s
• Generating functions
  • "THE MOST POWERFUL WAY to deal with sequences of numbers, as far as anybody knows, is to manipulate infinite series that 'generate' those sequences." --Graham, Knuth & Patashnik
  • Ordinary generating functions (ogf)
    Two perspectives:
    • Formal power series
    • Calculus-defined power series
  • Basic manipulations
    They're like polynomials of unbounded degree.
  • Dictionary of common ogfs: see esp. p. 161. (A copy of this will be provided with the exam.)