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 1:30-2:30 pm M, Tu, Th Lectures 10:00-11:00 am M, W, F 2301 Tolman Hall Textbook: Robert V. Hogg and Allen T. Craig, Introduction to Mathematical Statistics, 5th Edition, Upper Saddle River, New Jersey: Prentice Hall, 1995. 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, University 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. An independent effort and a serious attempt to set up and solve the problem will account for 75% of the score on each question. The remaining 50% of your grade will be your score on a final exam. This course is in Exam Group 1 (Wednesday, 12/10/03, 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 by the end of class on Friday of the week it is assigned. Any exceptions to this are noted on the course schedule that follows. Late homework can not be accepted in order that we can keep pace with the course schedule.ARE 210 Introduction to Mathematical Statistics page 2 COURSE SCHEDULE Week # 1 August 25-29 Topics Set theory, σ-algebras, probability set functions Readings Sections 1.1-1.3, pp. 1-19 Problems 1.1, 1.2, 1.7, 1.8, 1.12, 1.17, 1.23, 1.25 Week # 2 September 3-5 *No class on Labor Day, Monday, 9/1. Topics Mutually exclusive events, conditional probability, independence Readings Section 1.4, pp. 19-28 Problems 1.32, 1.33, 1.37, 1.39, 1.41 Week # 3 September 8-12 Topics Random variables Readings Sections 1.5-1.6, pp. 28-44 Problems 1.47, 1.48, 1.54, 1.55, 1.63, 1.66, 1.67 Week # 4 September 15-19 Topics Distribution functions, expectations, moment generating functions Readings Sections 1.7-1.9, pp. 44-67 Problems 1.75, 1.80, 1.87, 1.94, 1.96, 1.104, 1.115 Week # 5 September 22-26 *This is a short week (no class Friday). Homework due Wednesday. Topics Joint Distributions Readings Sections 2.1-2.2, pp. 74-91 Problems 2.1, 2.6, 2.13, 2.17 Week # 6 September 29 – October 3 Topics Correlation, independent random variables Readings Sections 2.3-2.5, pp. 91-115 Problems 2.21, 2.22, 2.23, 2.25, 2.28, 2.29, 2.33, 2.37ARE 210 Introduction to Mathematical Statistics page 3 Week # 7 October 6-10 Topics Binomial, Poisson, normal and chi-square distributions Readings Sections 3.1-3.5, pp. 116-154 Problems 3.7, 3.19, 3.46, 3.53, 3.54, 3.64, 3.72, 3.76 Week # 8 October 13-17 Topics Sampling theory, transformations of variables, t and F distributions Readings Sections 4.1-4.5, pp. 155-203 Problems 4.1, 4.26, 4.29, 4.49, 4.55 Week # 9 October 20-22 *This is a short week (no class Friday). Homework due Wednesday. Topics The moment generating function technique, the distributions of X and 22nS σ , the multivariate normal distribution Readings Sections 4.7-4.10, pp. 203-232 Problems 4.87, 4.92, 4.110, 4.125, 4.132 *Additional reading: Sections 10.1-10.3, 10.7-10.9, pp. 446-460, 478-496 Week # 10 October 27-31 Topics Point estimation, confidence intervals, hypothesis tests Readings Sections 6.1-6.4, pp. 259-286 Problems 6.1, 6.18, 6.28, 6.37, 6.38 Week # 11 November 3-7 Topics Qualities of estimators, sufficient statistics Readings Sections 7.1-7.3, pp. 307-329 Problems 7.1, 7.2, 7.4, 7.10, 7.21 Week # 12 November 10-14 *This may be a short week (possibly no class on Friday). Homework due Wednesday. Topics Completeness, uniqueness, the exponential class of distributions Readings Sections 7.4-7.5, 7.7, pp. 329-337, 341-347 Problems 7.25, 7.30, 7.31, 7.38, 7.48, 7.52ARE 210 Introduction to Mathematical Statistics page 4 Week # 13 November 17-21 *This may be a short week (possibly no class on Friday). Homework due Wednesday. Topics Fisher information, Cramér-Rao Lower Bound theorem Readings Section 8.2, pp. 372-380 Problems 8.11, 8.12, 8.16 Week # 14 November 24-26 *No class Friday – Thanksgiving break. Homework due Wednesday. Topics Neyman-Pearson Theorem, uniformly most powerful tests Readings Sections 9.1-9.2, pp. 395-412 Problems 9.7, 9.11, 9.17 Week # 15 December 1-5 Topics Wald, likelihood ratio, and Lagrange multiplier tests Readings Section 9.3, pp. 413-425 Problems 9.25, 9.29, 9.30, 9.33 FINAL EXAM Wednesday, December 10th, 8:00-11:00