ARE 210 Introduction to Mathematical Statistics page 1 ARE 210 INTRODUCTION TO MATHEMATICAL STATISTICS Instructor Jeffrey T. LaFrance Office 328 Giannini Hall Phone 643-5416 E-mail [email protected] Office Hours 1:00-2:00pm M, 1:30-2:30 Th Lectures 9:30-11:00am Tu, Th 2032 Valley LSB Textbook: Robert V. Hogg and Allen T. Craig, Introduction to Mathematical Statistics, 6th Edition, Upper Saddle River, New Jersey: Prentice Hall, 2004. This is a course in the elements of probability and mathematical statistics for the ph.D. sequence in quantitative methods in Agricultural and Resource Economics at the Univer-sity of California, Berkeley. An important component of the course is the weekly homework. These assignments are mandatory. Your aggregate score on them will account for 50% of your course grade. Attempt to complete each problem. Show your work neatly. The remaining 50% of your grade will be your score on a final exam. This course is in Exam Group 7 (Thursday, 12/16/04, 8:00-11:00 am). Hogg and Craig is a self-contained treatment of this subject matter at a level appropriate for seniors and 1st–year graduate students. The numerous examples in the text demon-strate the methodology and logic required for solving the problems at the end of each sec-tion. It is essential that you carefully read and understand the assigned material and work through the examples in each section of the text preceding the assigned problems at the end of that section before attempting the problems. To keep pace with the lectures and overall course schedule, it is important to complete at least one section of the textbook and the associated problems before each lecture. The weekly homework is due in class on Tuesday the week after it is assigned. Late homework will not be accepted in order that we can keep pace with the course schedule.ARE 210 Introduction to Mathematical Statistics page 2 TO BE CONTINUED … COURSE SCHEDULE Week # 1 August 30 – September 3 Topics Set theory, σ-algebras, probability set functions Readings Sections 1.1–.3, pp. 1–1 Problems 1.2.8, 1.2.9, 1.2.11, 1.2.13, 1.3.3, 1.3.5, 1.3.17 Week # 2 September 6 – 10 Topics Conditional Probability, Independence, Random Variables Readings Sections 1.4-1.5, pp. 22–40 Problems 1.4.1, 1.4.2, 1.4.10, 1.4.30, 15.2, 1.5.6, 1.5.8 Week # 3 September 13 – 17 Topics Discrete and Continuous Random Variables Readings Sections 1.6 – 1.7, pp. 41–53 Problems 1.6.3, 1.6.8, 1.7.1, 1.7.4, 1.7.7, 1.7.8, 1.7.12 Week # 4 September 20 – 24 Topics Expectation Readings Sections 1.8 – 1.10, pp. 53–72 Problems 1.8.3, 1.8.9, 1.8.14, 1.9.6, 1.9.13, 1.9.14, 1.10.1 Week # 5 September 27 – October 1 Topics Bivariate Distributions Readings Sections 2.1 – 2.2, pp. 73–93 Problems 2.1.1, 2.1.6, 2.1.12, 2.2.3, 2.2.4, 2.2.6 Week # 6 October 4 – October 8 Topics Conditional Distributions, Correlation, Independence Readings Sections 2.3 – 2.5, pp. 93–115 Problems 2.3.3, 2.3.5, 2.3.8, 2.4.7, 2.4.8, 2.5.6, 2.5.8 Week # 7 October 11 – October 15 Topics Multivariate Distributions Readings Sections 2.6 – 2.7, pp. 115–131 Problems 2.6.1, 2.6.2, 2.6.7, 2.7.1, 2.7.6 Week # 8 October 18– October 22ARE 210 Introduction to Mathematical Statistics page 3 TO BE CONTINUED … Topics Normal, Chi-Squared, T, and F Distributions Readings Sections 3.3 – 3.6, pp. 149–189 Problems 3.3.25, 3.4.21. 3.5.3, 3.6.10 Week # 9 October 25– October 29 Topics Properties of Estimators Readings Section 4.1, pp. 197–203 Section 5.1, pp. 233–238 Section 5.4, pp. 254–263 Problems 4.1.6, 4.1.14, 5.1.3,5.4.14 Week # 10 November 1– November 5 Topics Hypothesis Testing Readings Sections 5.5–5.7, pp. 263–286 Problems 5.4.25, 5.5.3, 5.5.8, 5.6.4, 5.6.10 Week # 11 November 8– November 12 Topics Maximum Likelihood Estimation and the Cramér-Rao Lower Bound Readings Sections 6.1–6.2, pp. 311–332 Problems 6.1.1, 6.1.3, 6.1.11, 6.2.1, 6.2.2, 6.2.8, 6.2.11, 6.2.14 (a) and (b) Week # 12 November 15– November 19 Topics Maximum Likelihood Tests and the Multiple Parameter Case Readings Sections 6.3–6.5, pp. 333–359 Problems 6.3.5, 6.3.13, 6.3.14, 6.4.2, 6.4.4, 6.5.2, 6.5.3, 6.5.4 Week # 13 November 30 (Thanksgiving Week) Topics Sufficiency Readings Section 7.1, pp. 367–373 Problems 7.1.1, 7.1.2 Week # 14 November 29– December 3 Topics Sufficient Statistics, Completeness, and Uniqueness Readings Sections 7.2–7.4, pp. 373–394 Problems 7.2.1, 7.3.3, 7.3.4 Week # 15 December 6 – December 10ARE 210 Introduction to Mathematical Statistics page 4 TO BE CONTINUED … Topics Optimal Tests Readings Sections 8.1–8.4, pp. 419–455 Problems 8.1.7, 8.2.3, 8.2.4, 8.2.7, 8.3.6, 8.3.8 FINAL EXAM: Thursday, 12/16/04, 8:00-11:00