MCS 341 EXAM 5: Final Examination
• When: Monday, December 20, 1:00-3:00 p.m.
• What: An examination consisting mostly of problems related to Chapter 6, Functions of Random Variables, Chapter 7, Sampling Distributions and the Central Limit Theorem, and supplementary class notes, but also problems related to earlier chapters.
• Where: Our classroom, Olin 219
• How: Closed-book, but with one 8 1/2"-by-11" sheet of paper with anything you want written on both sides.

TOPICS
• Functions of random variables
  • The method of distribution functions
  • The method of transformations
  • The method of moment-generating functions
  • Formulas for the distribution of X+Y, etc.
  • Order statistics, especially the minimum and maximum.
• Sampling distributions and the Central Limit Theorem
  • Our model for a random sample
  • The sampling distribution of the sample mean
    • in general
    • when the population is normal
  • The sampling distribution of the sample variance
  • The normal, chi-square, t, and F distributions
  • The Central Limit Theorem (CLT)
  • The method of proof of the CLT via moment generating functions
  • The normal approximation to the binomial distribution
• Some important topics from chapters 1-5
  • Probability and conditional probability
  • Random variables and their distributions
    • (Cumulative) distribution functions
    • Probability functions (discrete r.v.s)
    • Probability density functions (special continuous r.v.s)
  • Joint/multivariate probability distributions
    • Marginal and conditional distributions
    • Expected values, variances, covariances
  • Expected values (means), variances, other moments, and moment-generating functions
    • Definitions
    • Law of the Unconscious Statistician
    • Properties of expected values, variances, and covariances