STA2112F - Mathematical Statistics I (Fall, 1999)

http://utstat.toronto.edu/~brunner/2112F99

This course is designed for graduate students in Statistics and Biostatistics.

Content: Review of basic probability theory, distribution theory for normal samples, convergence of random variables, statistical models, sufficiency and ancillarity, statistical functionals, influence curves, maximum likelihood estimation, computational methods.

Instructor: Jerry Brunner (brunner@utstat.utoronto.ca).

Office Hours: Tuesday, Sid Smith 6022 (behind the mail room), 10:30-11:30 and 1-2.

Required Text: "Statistical Inference" by G. Casella and R. Berger, published by Wadsworth.

Texts on Reserve in the Math/Stat Library (Basement of Sidney Smith Hall):

• Hogg and Craig: Introduction to Mathematical Statistics - A traditional undergraduate text, about one step below our textbook.
• D. A. S. Fraser: Probability and Statistics - A non-traditional "undergraduate" text, about one step above our textbook.
• M. Spiegel: Schaumm's outline of advanced calculus - all you need to know, in compact format. Also for sale at the bookstore.
• W. Feller: Introduction to probability theory and its applications, Vol. 1 - A classic, useful for some homework problems.

Time and Place: Every Thursday from 9-12 a.m. in RW229

Prerequisites: Advanced calculus (eg. MAT239), linear algebra (eg. MAT223, MAT224), mathematical statistics (eg. STA257, STA261)

Evaluation: Mark will be based on weekly quizzes starting on Thursday Sept. 23d, and a final exam. Quizzes count for 70% and the final counts for 30%. Your lowest quiz mark will be dropped. No makeup quizzes will be given under any circumstances.

Quiz Marks 1-10

Assignments (Not to be handed in; do them in preparation for the quizzes)

• Quiz 1: Thursday September 23d., based on Parts 1 and 2 of the Review Assignment
• Quiz 2: Thursday September 30th., based on Parts 3 and 4 of the Review Assignment. Please use indicator functions!
• Quiz 3: Thursday October 7th, based on lecture material from September 16th, Textbook examples from Chapter 1, Exercises 1.1, 1.4, 1.5, 1.10, 1.13, 1.17*, 1.23*, 1.41, 1.44, 1.45, 1.52, 1.54, 1.56, 1.59, 1.60, 1.61, 1.62, 1.63, and some homework on limits of sequences
  • Limits Homework 1: PDF Version
  • Limits Homework 1: Postscript Version
• Quiz 4: Thursday Oct 14th
  • Text problems 2.8, 2.15, 2.16, 2.18, 2.19* (assume continuous, but it still gets a star), 2.26, 2.27, 1.62 (This is a repeat. Express as a mixed random variable and also draw a picture. I was able to make this problem fairly mechanical by writing V = 5 I{T<3} + 2T I{T>3}).
  • An infinite collection of random variables is sometimes called a stochastic process. Let X= (X₁,X₂, ... ) be a stochastic process in which X_n is a discrete random variable supported on the same set of 3 real numbers {a,b,c}, for  n = 1, 2, ....
    • What is the sample space inhabited by X?
    • Is this sample space countable or uncountable? Prove your answer.
• Quiz 5: Thursday Oct 21st
  • PDF Version of assignment
  • Postscript Version of assignment
• Quiz 6: Thursday Oct 28
  • PDF Version of assignment
  • Postscript Version of assignment
• Quiz 7: Thursday Nov 4th. Problems 3.25, 3.26, 3.28, 3.29, 3.30, 4.41, 4.43. Want a hint on problem 4.41c?
  • PDF Version of hint
  • Postscript Version of hint
• Quiz 9: Thursday Nov 18th.
  • PDF Version
  • Postscript Version
• Quiz 10: Thursday Nov 25th. Bring the convergence handout.
  • PDF Version
  • Postscript Version
• Quiz 11: Thursday Dec. 2nd. Bring the convergence handout.
  • PDF Version
  • Postscript Version

Handouts

• Indicator Handout
  • PDF Version
  • Postscript Version
• Epsilon-delta Notes
  • PDF Version
  • Postscript Version
• Mixed Distribution Handout
  • PDF Version
  • Postscript Version
  • LaTeX Version
• Math tools Handout
  • PDF Version
  • Postscript Version
  • LaTeX Version
• Convergence of Random Variables
  • PDF Version
  • Postscript Version
  • LaTeX Version

If you are connecting from a computer not located on campus, you may need to download Adobe Acrobat Reader (free software) in order to see mathematical text, including some assignments. You can get it from either of these locations; one may be busy.