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SYLLABUS FOR STATISTICS 100B - LECTURE 2 WINTER QUARTER 2011 Instructor: Nicolas Christou Office: 8931 Math Sciences Bldg. Telephone: (310) 206-4420 e-mail: [email protected] WWW: http://www.stat.ucla.edu/~nchristo/statistics100B Office hours: MWF 16:00 - 18:00, T 12:00 - 14:00 Lecture Lecture 2 Section 2A Day MWF Day T Class Time 15:00 - 15:50 Discussion Time 16:00 - 16:50 Location HUMANITIES 169 Location WGYOUNG 2200 RESOURCES: 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 Computational Resource (SOCR), freely available at: http://www.socr.ucla.edu. COURSE PREREQUISITES: Statistics 100A, or Mathematics 170A, or by instructor’s consent. COURSE TOPICS 1. 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 mean and 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 DESCRIPTION AND OBJECTIVES: Statistics 100B mainly deals with parameter estimation of various distributions. The problem is stated as follows: Suppose X1 , X2 , . . . , Xn are i.i.d. random variables from a distribution with pdf f (x; θ), where θ is unknown. Given this sample find an estimate of the parameter θ. We will also discuss properties of estimators, confidence intervals, and hypothesis testing. The t, χ2 , and F distributions will be discussed at the beginning of the course. They are very important in statistical inference. If time permits we will also discuss simple regression and correlation (this will be an introduction to Statistics 100C). COURSE POLICIES: Please remember to turn off cell phones. The use of laptop computers will not be permitted in class. You are expected to adhere to the honor code and code of conduct. If you have a disability that will require academic accommodation, please contact the UCLA Office for Students with Disabilities (OSD). COURSE GRADES: There will be four (4) quizzes, a final exam (cumulative), and homework or labs that will be assigned every week. Please write your name and staple your homework and labs. Late homework or labs will not be accepted and make-up exams will not be given. Being in class on time and fully participating is important for your understanding of the material and therefore for your success in the course. You are required to attend all the lectures. Attendance will be taken at random times during the course and it will count for 10% 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 + 0.10 × Quiz1 + 0.10 × Quiz2 0.10 × Quiz3 + 0.10 × Quiz4 + 0.40 × F inal Important dates: First day of classes: 03 January 2011. Last day of classes: 11 March. Holidays: 17 January (Martin Luther King, Jr.), 21 February (Presidents’ Day). Exams: Quiz 1: Week 3. Quiz 2: Week 4. Quiz 3: Week 6. Quiz 4: Week 8. Final: Week 10. Good Luck !!!