MATH 361: Mathematical Statistics I (sections 3428 and 3431)

2019 Fall, Emory University

Instructor: Dr. Le Chen
Email: le.chen@emory.edu
Office: Math & Science Center - E431
Office Hours: M 1:00pm-2:00pm and 3:00pm-4:00pm, W 2:00pm-3:00pm or by appointment.
Classroom Math & Science Center - W201
Class Meeting Times: MW, 8:30am-9:45am for class 3428, 10:00am-11:15am for class 3431.
Time period: Aug. 28, 2019 (first lecture) --- Dec. 9, 2019 (last class meeting)

Course Description: After an overview of finite probability theory, the course will deal primarily with continuous probability theory. Topics include distribution models (binomial, geometric, uniform, normal, Poisson, and exponential), the Chebyshev inequality, expectation, moment generating functions, the central limit theorem plus applications.
Textbook: Richard J. Larsen and Morris L. Marx, An Introduction to Mathematical Statistics and Its Application, Sixth Edition, by Prientice Hall.
Coverage: We will cover most of the following chapters

Chapter 1 -- Introduction
Chapter 2 -- Probability
Chapter 3 -- Random Variables
Chapter 4 -- Special distributions

Prerequisite: Math 210 or Math_OX 210 or Math 211 or Phys 211 or Math_OX 211 or Math 276 or equivalent transfer credit as prerequisite.

Note: The syllabus was created in Mar. 2019, and it is subject to changes during the semester.

Gradescope: We will be using Gradescope (gradescope.com) this term, which allows us to provide fast and accurate feedback on your work. Homework will be submitted through Gradescope, and homework and exam grades will be returned through Gradescope. As soon as grades are posted, you will be notified immediately so that you can log in and see your feedback. Your Gradescope login is your university email, and your password can be changed there. The same link can be used if you need to set your password for the first time. If you have any questions regarding Gradescope, please send your message to help@gradescope.com.
For registration, you should have received an email from gradescope. Otherwise, you may try the course entry code: 97X6WG.
Homework: Homework will be assigned weekly on both Gradescope and Canvas.

Only part of the problem set (randomly chosen) will be graded, however you will receive some credits for completing all homework problems.
Homework is usually due on Monday 1:00pm unless announced otherwise.
Solutions will normally be posted on Canvas on each Wednesday.
There will be about 11 assignments. The worst one will be dropped.
Please use Gradescope to upload your homework (preferably in pdf file). Login(s): netid@emory.edu.
Please do associate your solutions of each problem with pages on Gradescope.
Otherwise, you may end up with zero grade.
Here is a video that shows how to upload your homework to gradescope:

Attendence: You are expected to attend class regularly. You are responsible for all the materials presented and all the announcements made, if any, at each lecture.
Tests and Final: There will be two tests and one comprehensive final exam. Failure to take an exam during the scheduled class time will result in a score of zero for that exam. There will be no make-up exam except for well-documented reasons such as a medical emergency.
For the final exam, students who have conflicts (or more than 3 exams on Dec. 18) can schedule a "make-up" time. To reschedule the final exam, please contact me by the first test (Sept. 30).

Test 1: Wednesday, Oct. 9, in class.
Test 2: Monday, Nov. 11, in class.
Final: Wednesday, Dec. 18, 6:30pm-9:00pm, classroom ANTH 303.

Student with disabilities: If you have a disability and would like to request accommodations, please see me to discuss arrangements.
Calculators, laptops, tablets, phones: You may use a calculator such as a TI-83 Plus for doing calculations on the homework. However, calculators are not allowed on the midterms. All cellphones, PDAs, laptops, and any other devices with internet, phone or messaging capabilities must be turned off and put away at the beginning of each class. Laptops, tablets, and cell phones are only permitted when the devices are being required for an activity in class.
Honor Code: The Emory College Honor Code applies to all work in this class, including homework, the project, midterms and the final exam. See here for more information.

Grading Policy: There will be Homework (20%), two tests (25%+25%) and the final exam (30%).

A: 92% -- 100%, A-: 90% -- 91.9%.
B+: 87% -- 89.9%, B: 82% -- 86.9%, B-: 80% -- 81.9%
C+: 77% -- 79.9%, C: 72% -- 76.9%, C-: 70% -- 71.9%
D+: 67% -- 69.9%, D: 62% -- 66.9%, D-: 60% -- 61.9%
F: 0% -- 59%

Homework assignment: This section will be updated throughout this semester. Please refer this section for the actual assignments.

Homework 1.
§2.2: 2, 4, 10, 16, 18, 20, 26, 34, 36, 38.
§2.3: 2, 4, 10, 12, 14.
Homework 2.
§2.4: 2, 4, 8, 12, 16, 22, 26, 40.
§2.5: 2, 10, 14, 18, 20.
Homework 3.
§2.6: 14, 22, 32, 34, 38, 40, 44, 50, 54, 58, 60.
Homework 4.
§2.7: 2, 4, 14, 22.
§3.2: 2, 8, 18, 20, 26, 34.
Homework 5.
§3.3: 4, 10, 14.
§3.4: 2, 6, 8, 10, 16, 18.
§3.5: 8, 12, 18, 22, 26, 30, 36.
Homework 6.
§3.6: 2, 4, 10, 16, 22, 24.
Homework 7.
§3.7: 2, 6, 10, 11, 22, 26, 30, 36, 40, 42, 44.
§3.8: 2, 4.
Homework 8.
§3.8: 8, 12.
§3.9: 2, 8, 14, 18.
§3.11: 2, 4, 12, 20.
Homework 9.
§3.10: 2, 6, 12, 16.
§3.12: 2, 4, 8, 10, 14, 16, 20, 22.
Homework 10.
§4.2: 2, 6, 22, 24.
§4.3: 2, 8, 16, 18.
Homework 11.
§4.4: 2, 5, 6, 10.
§4.5: 2, 8, 10.
§4.6: 2, 5, 8.

Statistics for two midterm exams

Tentative schedule: Below is a week-by-week listing of the topics to be covered in class. Please note that this schedule is tentative. It may be necessary to make changes to the topics.

Monday	Wednesday
Aug. 26	Aug. 28 First day of class Introduction to Math 361 Sample spaces and the algebra of events (§2.2) §2.2: 2, 4, 10, 16, 18, 20, 26, 34, 36, 38.
Sept. 2 Labor Day, no class.	Sept. 4 Sample spaces and probability (§ 2.2-2.3) § 2.3: 2, 4, 10, 12, 14. Release the assignments for Homework 1.
Sept. 9 Conditional probability (§ 2.4) §2.4: 2, 4, 8, 12, 16, 22, 26, 40. Homework 1 due.	Sept. 11 Independence and repeated trials (§ 2.5) § 2.5: 2, 10, 18, 20, 26. Release the assignments for Homework 2.
Sept. 16 Combinatorics (§ 2.6) § 2.6: 14, 22, 32, 34, 38, 40. Homework 2 due.	Sept. 18 Combinatorics (§ 2.6) § 2.6: 44, 50, 54, 58, 60. Release the assignments for Homework 3.
Sept. 23 Combinatorial probability (§ 2.7) § 2.7: 2, 4, 14, 22 Homework 3 due.	Sept. 25 Random variables (§ 3.1 -3.2) Discrete random variables (§ 3.3) § 3.2: 6, 10, 22, 24, 26. Release the assignments for Homework 4.
Sept. 30 Discrete random variables (§ 3.3) Continuous random variables (§ 3.4) § 3.3: 4, 10, 14. § 3.4: 2, 6, 8, 10, 16, 18. Homework 4 due.	Oct. 2 Expected value (§ 3.5) § 3.5: 8, 12, 18, 22, 26, 30, 36. Release the assignments for Homework 5.
Oct. 7 Review for Exam 1. Homework 5 due.	Oct. 9 Exam 1.
Oct. 14 Columbus Day, no class.	Oct. 16 The variance (§ 3.6) § 3.6: 2, 4, 10, 16, 22, 24. Release the assignments for Homework 6.
Oct. 21 Joint densities (§ 3.7) § 3.7: 2, 6, 10, 11, 22, 26, 30, 36, 40, 42, 44. Homework 6 due.	Oct. 23 Transforming and combining random variables (§ 3.8) § 3.8: 2, 4. Release the assignments for Homework 7.
Oct. 28 Transforming and combining random variables (§ 3.8) Further properties of mean and variance (§ 3.9) § 3.8: 8, 12. § 3.9: 2, 8, 14, 18. Homework 7 due.	Oct. 30 Conditional densities (§ 3.11) § 3.11: 2, 4, 12, 20. Release the assignments for Homework 8.
Nov. 4 Moment generating functions (§ 3.12) § 3.12: 2, 4, 8, 10, 14, 16, 20, 22. Homework 8 due.	Nov. 6 Review for exam 2.
Nov. 11 Exam 2.	Nov. 13 Order Statistics (§ 3.10) § 3.10: 2, 6, 12, 16. Release the assignments for Homework 9.
Nov. 18 Poisson and Normal distributions (§ 4.2-4.3) Theory part. Homework 9 due.	Nov. 20 Poisson and Normal distributions (§ 4.2-4.3) Example part. § 4.2: 2, 6, 14, 18, 22, 28. § 4.3: 2, 8, 16, 18. Release the assignments for Homework 10.
Nov. 25 Gamma distribution (§4.6) § 4.6: 2, 5, 8. Homework 10 due.	Nov. 27 Thanksgiving break. No class.
Dec. 2 Geometric and negative binomial distributions (§ 4.4-4.5) § 4.4: 2, 5, 6, 10. § 4.5: 2, 8, 10. Release the assignments for Homework 11.	Dec. 4 Review for the final.
Dec. 9 Last day of class. Review for the final. Homework 11 due.	Dec. 11
Dec. 16	Dec. 18 Final Exam, 6:30pm-9:00pm