ST 501 Fundamentals of Statistical Inference I

Semester: Fall 2026

Lecture days/times: Tuesdays and Thursdays 15:00–16:15

Location: 2207 Gardner Hall

3 credit hours

Instructor

Teaching Assistant

Course Description: First of a two-semester sequence in probability and statistics taught at a calculus-based level. Probability: discrete and continuous distributions, expected values, transformations of random variables, sampling distributions. Credit not given for both ST 701 and ST 501.

Prerequisite: Calculus 3 (MA 242)

Learning Outcomes. By the end of the course, students will be able to:

1. Apply basic concepts of probability theory to logical reasoning about uncertain events.
2. Distinguish different types of random variables.
3. Ascertain properties of random variables.
4. Formulate mathematical proofs based on axioms and techniques of probability calculus.
5. Apply limit theorems to approximate the behavior of random phenomena.

Required Text:

Casella and Berger (2024). Statistical Inference, 2nd edition. CRC Press and Chapman and Hall.

Digital Course Components:

Course website: https://jonathanpw.github.io/ST501

Grade Distribution:

Attendance	25%
Exam 1	20%
Exam 2	20%
Final exam	35%

Letter Grade Distribution:

≥ 93.00	A	73.00 - 76.99	C
90.00 - 92.99	A-	70.00 - 72.99	C-
87.00 - 89.99	B+	67.00 - 69.99	D+
83.00 - 86.99	B	63.00 - 66.99	D
80.00 - 82.99	B-	60.00 - 62.99	D-
77.00 - 79.99	C+	≤ 59.99	F

For students taking the course as credit-only, S is equivalent to C- or better; otherwise U.

No expectations beyond attendance apply to students choosing to audit the course.

Exam Schedule

Exam 1: Thursday, 24 September 2026

Exam 2: Thursday, 5 November 2026

Final exam: 15:30–18:00 Thursday, 3 December 2026

Personal note to students: Please do not feel intimidated about interacting with me. Regardless of how busy or stressed I may appear to you, teaching your class is a part of my job, and I take that very seriously. I care deeply about the quality of your learning. Please always reach out to me if you have questions, concerns, or need help. I understand that it can be difficult and can even feel embarrassing to ask for help. However, I was once in your position, and I promise to always treat you with respect, empathy, and kindness. Nobody that ever did anything meaningful did so without first failing over and over again.

Course policies and commentary:

• Exams
  • There will be two midterm exams and a final exam.
  • All exams are closed-book and closed-notes. A simple calculator (capable only of basic arithmetic) is permitted but not necessary.
• Assignments
  • Practice homework problems will be assigned each Tuesday evening. These problems will be relevant (if not identical) to the exam questions.
  • Take responsibility for understanding solutions to all practice problems. For example, if you find a solution on StackExchange, then convince yourself that the solution is actually correct.
  • Learn to distinguish between the things you do know and the things you do not know (this is one of the most important results of all education). To understand, to a particular degree, that a given statement is true means that you can explain why the statement is true, to the particular degree.
• Attendance
  • Attendance is recorded; each lecture counts as 1% of the course total. Please sign the attendance sheet each class, beginning on the second lecture of the semester.
  • Use lecture time as you feel most productive, but do not use it in a way that is distracting to others.
  • Lecture time is not for answering homework questions; please attend the lab or office hours for homework questions.
• Class recording statement
  • No components of this course will be recorded.

Tentative Course Outline: Chapters 1–5 of Statistical Inference by Casella and Berger, Second Edition, published 2024.

• Probability theory introduction topics
• Discrete random variables
• Continuous random variables
• Multivariate probability
• Functions of random variables
• Sampling distributions
• Central limit theorem

NCSU Policies, Regulations, and Rules:

Students are responsible for reviewing the NC State University Policies, Rules, and Regulations (PRRs), which pertain to their course rights and responsibilities, including, but not limited to:

• POL 04.25.05 Equal Opportunity and Non-Discrimination Policy Statement
  • REG 02.20.01 Academic Accommodations for Students with Disabilities
• POL 11.35.01 Student Conduct
  • REG 11.35.05 Code of Student Conduct
  • REG 11.35.02 Student Discipline Procedures
• REG 02.20.03 Attendance Regulations
• REG 02.50.03 Grades and Grade Point Average
• REG 02.20.15 Credit-Only Courses
• REG 02.20.04 Audits
• REG 08.00.11 Online Course Material Host Requirements

This course engages diverse scholarly perspectives to develop critical thinking and analysis. A debate and inclusion of a reading or media does not imply endorsement. A syllabus does not constitute an express or implied contract among the student, faculty, or institution. Rather, it serves as a guide for the course. This syllabus may be modified according to course needs.