**Course: Math 408, Mathematical Statistics, Fall 2023**

**Prerequisite:** Math 407, Probability Theory.

**Course Content:** Principles for testing hypotheses and estimation, confidence intervals, methods of moments, maximum likelihood, information inequality, likelihood ratio tests, goodness of fit and nonparametric methods.

*Last update:* 9 May 2023

**Instructor:** Steven Heilman, stevenmheilman(@-symbol)gmail.com

**Office Hours:** Tuesdays, 9AM-11AM, on zoom [link posted in blackboard]

**Lecture Meeting Time/Location:** Mondays, Wednesdays, and Fridays, 1PM-150PM, KAP 156

**TA:** Tianle Liu, tianleli(@-symbol)usc.edu

**TA Office Hours:** Held in the Math Center, with schedule provided at that link.

**Discussion Section Meeting Time/Location**:

- 39520, Tuesdays and Thursdays, 12PM-1250PM, KAP 167
- 39521, Tuesdays and Thursdays, 1PM-150PM, KAP 148

**Textbook: **The following textbook is recommended but **not required**.

Rice, __Mathematical Statistics & Data Analysis__.

**Exam 1**: Wednesday, September 27, 1PM-150PM, KAP 156

**Exam 2**: Friday, November 3, 1PM-150PM, KAP 156

**Final Exam**: Wednesday, December 13, 11AM-1PM, Location TBD

**Other Resources:** Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments

**Email Policy:**

- My email address for this course is stevenmheilman@gmail.com
- It is your responsibility to make sure you are receiving emails from stevenmheilman@gmail.com , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from this syllabus.

**Exam Procedures**: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)

Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.

https://osas.usc.edu/

213-740-0776 (phone)

213-740-6948 (TDD only)

213-740-8216 (fax)

OSASFrontDesk@usc.edu

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the *Office of Equity and Diversity* http://equity.usc.edu/ or to the *Department of Public Safety* http://capsnet.usc.edu/department/department-public-safety/online-forms/contact-us. This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. *The Center for Women and Men* http://www.usc.edu/student-affairs/cwm/ provides 24/7 confidential support, and the sexual assault resource center webpage sarc@usc.edu describes reporting options and other resources.

**Exam Resources**: Here are exams from the last time I taught 408: Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution. Some past 408 exams appear here, near the bottom of the page. Some practice exams for a course similar to ours appear here, here, and here

**Homework Policy**:

- Homeworks are
**due at 12PM noon Thursdays**, i.e. at the beginning of the first discussion session on Thursdays. - Homeworks are submitted in Gradescope. To avoid internet issues, I recommend making your first submission of an assignment well in advance of the deadline.
- Homeworks should be submitted as single PDF documents. One way to create a PDF document from paper homework assignments is the freely available Adode Scan App
- Late homework is
**not accepted**. - If you still want to turn in your homework late, then the number of minutes late divided by ten will be deducted from the homework score. The exact deduction and rounding procedure is not guaranteed to be accurate.
- The
**single lowest**homework score will be dropped. This policy is meant to account for illnesses, emergencies, dropped internet connections, etc. - You may not use the internet to try to find answers to homework problems.
- Do not submit homework via email.
- Collaboration on homeworks is allowed and encouraged.
- All homework assignments must be written by you, i.e. you cannot copy someone else`s solution verbatim.

**Quiz Policy**

- There will be several quizzes throughout the semester, as listed in the schedule below, roughly every other week. One week before the quiz occurs, a list of quiz problems will be posted on the course website. The quiz will have a few problems similar or identical to the posted list of problems.
- The
**single lowest**quiz score will be dropped. This policy is meant to account for illnesses, emergencies, etc. - Quizzes will be administered in your discussion section on Thursday. Each quiz should last about 10-15 minutes.
- No notes, no books, no calculators, etc. will be allowed during the quizzes.

**Grading Policy:**

- The final course grade is weighted as the larger of the following two schemes.
- Scheme 1: class participation (3%), homework (11%), quizzes (11%), the first midterm (20%), the second midterm (20%), and the final (35%).
- Scheme 2: class participation (3%), homework (11%), quizzes (11%), the largest midterm grade (30%), and the final (45%).

- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- Class participation is not the same as attendance. I will never explicitly take attendance, but I will notice if someone is frequently absent. Things that increase your class participation grade include: asking good questions, paying attention in class, showing up on time or early to class, etc. Things that decrease your class participation grade include: excessive talking or disruptions during class, frequent absences, excessive texting/smartphone usage in class, frequent tardiness, etc.
- You must take the final exam to pass the course.

Tentative Schedule: (This schedule may change slightly during the course.)

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Aug 21: Review of Probability | Aug 22 | Aug 23: 5.3, Review of Probability | Aug 24: Homework 1 due | Aug 25: 6.2, 6.3, Review of Probability |

2 | Aug 28: 7.3, Review of Probability | Aug 29 | Aug 30: 8.1, 8.2, Parameter Estimation | Aug 31: Quiz 1 | Sep 1: 8.3, Parameter Estimation |

3 | Sep 4: No class | Sep 5 | Sep 6: 8.4, Method of Moments | Sep 7: Homework 2 due | Sep 8: 8.5, Maximum Likelihood Estimation |

4 | Sep 11: 8.6, Efficiency, Cramer-Rao | Sep 12 | Sep 13: 8.7, Sufficiency, Rao-Blackwell | Sep 14: Quiz 2 | Sep 15: 9.1, 9.2, Hypothesis Testing |

5 | Sep 18: 9.2, Likelihood Ratio Tests | Sep 19 | Sep 20: 9.3, Neyman-Pearson Lemma | Sep 21: Homework 3 due | Sep 22: 9.4, Confidence Intervals |

6 | Sep 25: 9.4, Confidence Regions/Hypothesis Tests | Sep 26 | Sep 27: Exam 1 | Sep 28: No homework due | Sep 30: 9.4, p-values |

7 | Oct 2: 9.5, Generalized Likelihood Ratio Test | Oct 3 | Oct 4: 8.2, Case Study: Alpha Particles, Contingency Tables | Oct 5: Quiz 3 | Oct 6: 8.2, Case Study: Alpha Particles, Contingency Tables |

8 | Oct 9: 8.2, Case Study: Alpha Particles, Contingency Tables | Oct 10 | Oct 11: 11.2, Comparing Independent Gaussians | Oct 12: Homework 4 due,No class | Oct 13: No class |

9 | Oct 16: 11.2, Comparing Independent Samples | Oct 17 | Oct 18: 11.2, Comparing Independent Samples | Oct 19: Quiz 4 | Oct 20: 11.3, Comparing Dependent Samples |

10 | Oct 23: 12.2, Analysis of Variance | Oct 24 | Oct 25: 12.2, Analysis of Variance | Oct 26: Homework 5 due | Oct 27: 14.2, Linear Regression |

11 | Oct 30: 14.2, Linear Regression | Oct 31 | Nov 1: 14.2, Linear Regression | Nov 2: No homework due | Nov 3: Exam 2 |

12 | Nov 6: 14.3, 14.4, Least Squares | Nov 7 | Nov 8: 14.3, 14.4, Least Squares | Nov 9: Quiz 5 | Nov 10: No class |

13 | Nov 13: Leeway | Nov 14 | Nov 15: Leeway | Nov 16: Homework 6 due | Nov 17: Leeway |

14 | Nov 20: Leeway | Nov 21 | Nov 22: No class | Nov 23: No class | Nov 24: No class |

15 | Nov 27: Review of course | Nov 28 | Nov 29: Review of course | Nov 30: Quiz 6 | Dec 1: Review of course |

**Advice on succeeding in a math class:**

- Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
- When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
- Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

**Homework**

**Homework .tex files**

**Quiz Problems**

**Exam Solutions**

**Supplementary Notes**