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Math 3081 Probability and Statistics Spring 2016 Instructor: Hanai Sadaka Office: 543 NI Phone: 617-373-4882 (Math Dept. Office: 373-2450) Email: [email protected] Office Hours: Mondays and Wednesdays: 2:45-4:15 or by appointment Text: “An Introduction to Mathematical Statistics and its Applications”, R. Larsen and M. Marx, fifth edition. (Published by Prentice Hall). Grading: Quizzes --- 20%; Two in-class exams --- 40%; Final Exam --- 40% 93-100 A 90-92 A87-89 B+ 83-86 B 80-82 B73-76 C 70-72 C67-69 D+ 63-66 D 60-62 D 77-79 C+ 0-59 F There will be 4 quizzes, two 1 hour tests and a final exam. The final will be cumulative. Borderline grades are determined by the final exam score. One lowest quiz score is dropped. This is an introduction course to the theory of probability and statistics. Its goal is to develop the mathematical tools and concepts necessary for modeling uncertainty and data analysis in real-world problem. This is a Calculus-based course, and assumes a working knowledge of single-variable calculus as well as some acquaintance with multi-variable calculus (including multiple integration). IMPORTANT: 1. The best way to learn this material is to do the homework problems every week. Please ask me questions about things you don’t understand, either in class or at my office. DON’T wait until you feel completely lost! 2. It is your responsibility to be aware of any changes the instructor may make to the syllabus as they are announced in class, or as posted on the course webpage. Students are responsible for all information given when they are absent. 3. The grade I (Incomplete) will be given only if you have a good attendance record, have missed the Final for a good reason, and otherwise are doing passing work. Makeup exams are not given unless you have missed the exam for a valid reason and can prove it. Both makeups and incomplete are given at the discretion of the instructor. 4. Cheating will not be tolerated. All incidents of cheating will be reported to the Office of Judicial Affairs. The University’s cheating policy and related disciplinary actions are detailed in the Student Handbook. The Handbook also includes a description of what is considered cheating by the University. Cheating in this class includes (but is not limited to): looking at the papers of others during a quiz or test, talking to other students during a quiz or test. 5. If you have issues with this course and/or instructor which you are not comfortable discussing with your instructor, you should contact the course coordinator, Hanai Sadaka, at [email protected]. For any matters that remain unresolved, contact the Teaching Director, Prof. Massey, at [email protected]. 6. As a matter of Math Department policy, the I grade (incomplete) will be given only rarely. It is intended to cover real emergency situations in which a student who is doing reasonably well (C- or better) is unable, due to circumstances beyond the student's control, to complete all course requirements (e.g., is unable to take the final exam due to hospitalization). An I grade may not be used to rescue a failing grade, or to postpone the final. 7. All students without legitimate conflicts will take the final exam at the scheduled date and time. Do not make travel plans that conflict with the final exam. 8. The last day to drop a course without a W grade is Monday February 1. The last day to drop a course with a W grade is Thursday April 21. The last day to file a Final Exam Conflict Form is Wednesday February 3. 9. Please complete the TRACE evaluations at the end of the course. Class Schedule & Homework List Please note that the schedule is very tentative and may be changed at any point. Students are responsible for coming to class and if absent, students still need to be responsible for all material covered and changes announced in class. It is the students’ responsibility to check emails and Blackboard. Week Jan. 11-14 Sec. 2.1 2.2 2.3 2.4 Topic Introduction Sample Spaces and the Algebra of Sets The Probability Function Conditional Probability Assignment 2.4 2.5 3.2 3.3 31, 34, 39, 40, 42, 46, 52 11, 12, 16, 18, 19, 20, 23, 25 4, 7, 8, 9, 23 1, 4, 5, 7, 13, 14 2, 3, 13, 16, 22, 26 1, 2, 4, 6, 9, 12 1, 2, 7, 12, 16, 21, 24, 25, 26 Jan. 25-28 3.3 3.4 Continued Independence Binomial Probabilities Discrete Random Variables 1/18 Martin Luther King Day: No Classes Continued Continuous Random Variables Feb. 1-4 3.5 3.6 Expected Values The Variance 1, 8, 12, 18, 20(a), 27 2, 5-8, 11 Feb. 8-11 3.7 3.9 Joint Densities Further Properties of the Mean and Variance The Poisson Distribution The Normal Distribution Exam Review 2/15 President’s Day, no classes 1, 8, 10, 17, 19, 23, 40, 45 13, 16, 17, 20 Jan. 18-21 Feb. 15-18 4.2 4.3 Feb. 22-25 4.3 Feb. 29-Mar. 3 5.2 5.3 Mar. 7-11 Mar. 14-17 Mar. 17-21 Mar. 21-24 Mar. 28-31 Apr 4-7 Apr.11-14 Apr. 18-21 Abr. 22-29 First 1 hour exam on Feb. 19 Continued Estimating Parameters Interval Estimation Spring Break 5.3 5.4 Continued Properties of Estimators 6.2 6.3 6.4 7.2 7.3 7.4 7.5 9.2 The Decision Rule –hypothesis tests Testing Binomial Data Type I and Type II Errors The t-distribution Deriving the t-distribution Drawing Inferences about Drawing Inferences about Testing : Exam Review Second 1 hour exam on April 7 The F-test Binomial Data: Testing : Review 4/18 Patriot Day, no class Review 4/21 Reading Day, no class 9.3 9.4 Final Exams Quiz 1 Thursday Jan. 21 1, 3, 5, 8-10 Quiz 2 Thursday Feb. 4 10, 17, 20, 21 2, 5, 8, 14, 16, 17, 21, 22 27, 30, 33, 35 Exam 1 Wednesday Feb. 25 1, 3-7, 10, 11 1, 2, 4, 5, 11, 14, 26 5, 9, 11 1, 3, 4, 6, 7, 9, 10, 11 1-4, 6 1, 4, 5, 7, 8, 9, 10 13 1, 2, 7-9, 12 Quiz 3 Thursday Mar. 17 Quiz 4 Thursday Mar. 24 1-10 2-5, 7 1-5 Exam 2 Monday Apr. 7