**Course: Math 307, Statistical Inference and Data Analysis I, Fall 2022**

**Prerequisite:** MATH 118gx or MATH 125g or MATH 126g or MATH 127 or MATH 129

**Course Content:** Probability, counting, independence, distributions, random variables, simulation, expectation, variance, covariance, transformations, law of large numbers, Central limit theorem, estimation, efficiency, maximum likelihood, Cramer-Rao bound, bootstrap.

*Last update:* 1 November 2022

**Instructor:** [as of October 13] Steven Heilman, stevenmheilman(@-symbol)gmail.com

**Office Hours:** Tuesdays, 8AM-9AM and 10AM-11AM, on zoom [link posted on blackboard]

**Lecture Meeting Time/Location:** Mondays, Wednesdays, and Fridays, 1PM-150PM, WPH 102

**TA:** Bo Wu, bwu168(@-symbol)usc.edu

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

**Discussion Section Meeting Time/Location**: Tuesdays and Thursdays, 9AM-950AM, KAP 147

**Textbook:** __A First Course in Probability__, 9th Edition, Sheldon Ross

__Mathematical Statistics with Applications__, Wackerly et al.

**Exam 2**: Wednesday, November 2, 1PM-150PM, WPH 102

**Final Exam**: Wednesday, December 14, 11AM-1PM, Location TBD

**Other Resources:** 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 the exams I used when I previously taught 407: Exam 1 Exam 1 Solution Exam 1v2 Exam 1v2 Solution Exam 2 Exam 2 Solution Exam 2v2 Exam 2v2 Solution Final Final Solution Finalv2 Finalv2 Solution Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Here is a page containing old exams for another similar class. Here is a practice midterm (with solutions). Here are some more exams from a second quarter probability course: Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution. Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions. Here are some exams from when 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 408 appear here, here, and here

Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order.

**Grading Policy**

- The final course grade is weighted as the larger of the following two schemes
- Scheme 1: HW: 10%; Quizzes: 15%; Midterms: better score with 25%, lower score with 15%; Final 35%.
- Scheme 2: HW: 10%; Quizzes: 15%; Midterms: better score with 25%, lower score with 10%; Final 40%.

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

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

9 | Oct 17: 6.2, Independent Random Variables | Oct 18 | Oct 19: 6.3, Sums of Independent Random Variables | Oct 20 | Oct 21: 6.7, Joint PDFs |

10 | Oct 24: 7.2, Sums of Random Variables | Oct 25 | Oct 26: 7.4, Covariance, Variance of Sums, Correlation | Oct 27 | Oct 28: 7.7, Moment Generating Function, 8.1, Limit Theorems |

11 | Oct 31: 8.2, Chebyshev's Inequality and the Weak Law | Nov 1 | Nov 2: Exam 2 | Nov 3 | Nov 4: 8.3, Central Limit Theorem |

12 | Nov 7: 8.1, Estimation [Wackerly et al book] | Nov 8 | Nov 9: 8.2, Bias, Mean Squared Error | Nov 10 | Nov 11: No class |

13 | Nov 14: 8.3, Unbiased Estimation | Nov 15 | Nov 16: 9.2 Efficiency | Nov 17 | Nov 18: 9.6, Method of Moments |

14 | Nov 21: 9.7, Maximum Likelihood | Nov 22 | Nov 23: No class | Nov 24: No class | Nov 25: No class |

15 | Nov 28: 9.8, Maximum Likelihood, Cramer-Rao | Nov 29 | Nov 30: 9.8, Cramer-Rao | Dec 1: | Dec 2: 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. Also, I would very much recommend typesetting your homework. Learning LaTeX is a very important skill to have for doing mathematics. Here is a template .tex file if you want to get started typesetting.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

** **

**Exam Solutions**

**Supplementary Notes**