SYLLABUS FOR STATISTICS 100B - LECTURE 3INTRODUCTION TO MATHEMATICAL STATISTICSWINTER QUARTER 2012Instructor: Nicolas ChristouOffice: 8931 Math Sciences Bldg.Telephone: (310) 206-4420e-mail: [email protected]: http://www.stat.ucla.edu/~nchristo/statistics100BOffice hours: MWF 16:00 - 18:00, T 12:00 - 14:00Lecture Day Class Time LocationLecture 3 MWF 12:00 - 12:50 FRANZ 2258ASection Day Discussion Time Location3A R 15:00 - 15:50 ROYCE 156RESOURCES:Textbook (optional): John Rice, Mathematical Statistics and Data Analysis, Third Edition, Duxbury Press,2006.Probability and Statistics EBook (freely available at):http://wiki.stat.ucla.edu/socr/index.php/EBook.Software: R (can be downloaded freely from http://cran.stat.ucla.edu), and Statistics Online Compu-tational Resource (SOCR), freely available at: http://www.socr.ucla.edu.COURSE PREREQUISITES:Statistics 100A, or Mathematics 170A, or by instructor’s consent.COURSE DESCRIPTION AND OBJECTIVES:Statistics 100B mainly deals with parameter estimation of various distributions. The problem is stated asfollows: Suppose X1, X2, . . . , Xnare i.i.d. random variables from a distribution with pdf f(x; θ), where θis unknown. Given this sample we would like to find an estimate of the parameter θ. We will also dis-cuss properties of estimators, confidence intervals, and hypothesis testing. The t, χ2, and F distributionswill be discussed at the beginning of the course. They are very important in statistical inference. If timepermits we will also discuss simple regression and correlation (this will be an introduction to Statistics 100C).COURSE TOPICS1. Statistics 100A quick review.2. Simulations: Techniques for simulating continuous random variables.3. Moments, and moment generating functions.4. Moments of linear combinations of random variables and covariance between two random variables.5. Chebyshev’s inequality.6. The Central Limit Theorem and the Law of Large Numbers. The distribution of the sample meanand sum of n observations.7. The Chi-Square distribution and the distribution of the sample variance. The F and t distributions.8. Estimation and properties of estimators. Method of moments and method of maximum likelihood.Cramer-Rao inequality, Rao-Blackwell theorem.9. Confidence intervals for means and proportions.10. Hypothesis testing. Neyman-Pearson lemma, power functions and likelihood ratio tests.11. Regression and correlation.COURSE POLICIES:Please remember to turn off cell phones. The use of laptop computers will not be permitted in class. Youare expected to adhere to the honor code and code of conduct. If you have a disability that will requireacademic accommodation, please contact the UCLA Office for Students with Disabilities (OSD).COURSE GRADES:There will be two (2) midterms, a final exam (cumulative), and homework or labs that will be assignedevery week. Please write your name and staple your homework and labs. Late homework or labs will not beaccepted and make-up exams will not be given. Being in class on time and fully participating is importantfor your understanding of the material and therefore for your success in the course. You are required toattend all the lectures. Attendance will be taken at random times during the course and it will count for10% of your grade. The tentative dates for the exams are shown below.The course grade will be based on the calculation:F inal score = 0.10 × Attendance + 0.10 × Homework/Labs+ 0.20 × M idterm1 + 0.20 × Midterm2 + 0.40 × F inalCommunication:In-class handouts can be accessed at http://www.stat.ucla.edu/~nchristo/statistics100B.Please keep a current e-mail address with my.UCLA.edu in order to receive class announcements and re-minders.Important dates:First day of classes: 09 January 2012.Last day of classes: 16 March.Holidays: 16 January (Martin Luther King, Jr.), 20 February (Presidents’ Day).Exams:Exam 1: Week 4.Exam 2: Week 7.Final: Week 10.Good Luck