MA395-A Final Exam Study Guide

The final will be comprehensive, including:

• The following material from the text:
  • Chapter 2
  • Chapter 3 (excluding Section 10)
  • Chapter 4 (excluding Section 11)
  • Chapter 5
  • Chapter 6 (excluding Section 6)
  • Chapter 7 Selected material:
    • Theorem 7.1
    • The definitions of the t and F distributions
    • The central limit theorem (the slightly simplified form stated in the proof posted in notes and handouts is OK)
• The following supplemental material (posted in the notes and handouts section)
  • The multivariate normal density function
  • The variance-covariance matrix
  • Expectation, variance, and covariance of linear combinations of random variables
  • Quadratic forms and their relation to the chi-square distribution
  • The proof of the central limit theorem (also posted under notes and handouts)

• Section 1: A matching section with terms definitions
• Section 2: Proofs. This section will contain:
  • A proof you have seen before - choose one of the following:
    • Prove that all covariances being zero is a sufficient condition for multivariate normal variates to be independent (see the supplementary material posted in the notes and handouts section)
    • Prove the central limit theorem (a proof with more detail than required is posted in the notes and handouts section)
  • Two additional short proofs. These be along the lines of : Show that E(x-u)^2=E(X^2)-[E(x)]^2
• Section 3: Applications (15 problems choose 12) These will be similar to the problems on the assignments. The best way to prepare for this part of the exam is to review the solutions to the assignments (especially the more recent ones). Time constraints dictate that the problems on the exam have to be less difficult (on average) than those in the assignments, so if you know how to do the assigned problems, you should be well prepared.

All formulas listed inside the back cover of the text will be supplied, in addition to the equivalent expressions for the multivariate normal distribution (density function, moment-generating function). Any formulas needed from the supplementary material will also be supplied.