Math 466 - Theory of Statistics

Syllabus for Math 466, Section 003, Spring 2024

Location and Times

Math 466, Section 002, meets in C E Chavez Bldg, Rm 104, TuTh 12:30-12:45pm.

Course Description

According to the catalogue:

Sampling theory. Point estimation. Limiting distributions. Testing Hypotheses. Confidence intervals. Large sample methods.

Course Prerequisites or Co-requisites

MATH 464 - Theory of Probability.
or equivalent coursework with instructor permission.

Instructor and Contact Information

Information	Data
Instructor	Professor Marek Rychlik
Office	Mathematics 605
Telephone	1-520-621-6865
Email	rychlik@arizona.edu
Instructor Homepage/Web Server	http://alamos.math.arizona.edu
Course Homepage	http://alamos.math.arizona.edu/math466
Course Homepage (Mirror)	http://marekrychlik.com/math466

Office Hours

Semester: Spring, 2025

Personnel	Day of the Week	Hour	Room	Comment
Marek Rychlik	Monday	5:30pm-6:30pm	Math 589B Zoom Link	Upper Division Tutoring
Novel Dey, Math 589 Super-TA	Monday	1:00pm-2:00pm	Zoom	Math 589 Super-TA office hours (Zoom link in D2L menu)
Marek Rychlik	Wednesday	5:00pm-6:00pm	Math 589 Zoom Link	Regular office hours

Office hours by appointment are welcome. Please contact me by e-mail first, so that I can activate a Zoom link for the meeting.

Course Format and Teaching Methods

The course format is that of a conventional lecture, with in-class discussion and additional web-delivered content. All lectures will be recorded and available on Zoom and Panopto.

Written homework will be assigned regularly and graded using Gradescope.

In addition, the course incorporates required programming assignments. Numerical experimentation is essential to understanding and using the course subject matter. The assignments will be graded by an autograder implemented in Gradescope.

Course Objectives

This course is an introduction to the theory of stochastics. The student will gain understanding of the following fundamental concepts:

Sampling theory
Point estimation
Limiting distributions
Testing Hypotheses
Confidence intervals
Large sample methods

Learning outcomes

Students who successfully complete this course are expected to be able to:

In the context of sampling distributions calculate and interpret confidence intervals.
Define and use consistency, efficiency, and sufficiency for point estimators.
Apply the method of moments.
Use method of maximum likelihood to derive optimal statistics.
Derive and apply t-tests and z-tests.

Generative AI use IS permitted or encouraged

In this course you are welcome and expected to use generative artificial intelligence/large language model tools, e.g. ChatGPT, Dall-e, Bard, Perplexity. Using these tools aligns with the course learning goals such as developing writing and programming skills, and ability to effectively use available information. Be aware that many AI companies collect information; do not enter confidential information as part of a prompt. LLMs may make up or hallucinate information. These tools may reflect misconceptions and biases of the data they were trained on and the human-written prompts used to steer them. You are responsible for checking facts, finding reliable sources for, and making a careful, critical examination of any work that you submit. Your use of AI tools or content must be acknowledged or cited. If you do not acknowledge or cite your use of an AI tool, what you submit will be considered a form of cheating or plagiarism. Please use the following guidelines for acknowledging/citing generative AI in your assignments:

Absence and Class Participation Policy

Importance of attendance and class participation

Participating in course and attending lectures and other course events are vital to the learning process. As such, attendance is required at all lectures and discussion section meetings. Students who miss class due to illness or emergency are required to bring documentation from their healthcare provider or other relevant, professional third parties. Failure to submit third-party documentation will result in unexcused absences.

Missed Exams

Students are expected to be present for all exams. If a verifiable emergency arises which prevents you from taking an in-class exam at the regularly scheduled time, the instructor must be notified as soon as possible, and in any case, prior to the next regularly scheduled class. Make-up exams and quizzes will be administered only at the discretion of the instructor and only under extreme circumstances. If a student is allowed to make up a missed exam, (s)he must take it at a mutually arranged time. No further opportunities will be extended. Failure to contact your instructor as stated above or inability to produce sufficient evidence of a real emergency will result in a grade of zero on the exam. Other remedies, such as adjusting credit for other exams, may be considered.

COVID-19 related policies

As we enter the semester, the health and wellbeing of everyone in this class is the highest priority. Accordingly, we are all required to follow the university guidelines on COVID-19 mitigation. Please visit http://www.covid19.arizona.edu for the latest guidance.

UA policies

The UA's policy concerning Class Attendance, Participation, and Administrative Drops is available at: http://catalog.arizona.edu/2015-16/policies/classatten.htm The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable, http://policy.arizona.edu/human-resources/religious-accommodation-policy . Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: http://uhap.web.arizona.edu/policy/appointed-personnel/7.04.02

Required Texts or Readings

Required Textbook

Mathematical Statistics with Applications. 7th Edition. Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Optional Reference Textbook

Introduction to probability theory. Hoel, Paul G., Stone, Charles J., Port, Sidney C.

Assignments and Examinations

Notes on exam administration

All examinations are planned to be administered during the class time, either in person or on Zoom.

If, due to unforseen circumstances, they cannot be held in person, they are held on Zoom using the "gallery view" mode.The exam papers for not in-person tests will be distributed on-line by D2L and collected electronically using D2L "dropbox" feature.

Exam/assignment listing with date and grade contribution

Exam or Assignment	Date	Grade contribution
Midterm 1	February 15 (Thursday), 12:30pm - 1:45pm	20%
Midterm 2	April 11 (Thursday), 12:30pm - 1:45pm	20%
Final Examination	May 8 (Wednesday), 1:00pm - 3:00pm	30%
Homework	See D2L	30%

Homework Assignments

Written homework consists of approximately twelve assignments equally contributing to the grade, each worth 30/12 = 2.5% of the grade. The assignments are posted on line at this link: Homework. The assignment papers are collected via Gradescope, which is cloud-based software for semi-automatic grading. Things to keep in mind:

The student will submit all graded work through Gradescope. Gradescope assignments, by their nature, are answer-oriented. The opportunity for partial credit is somewhat limited.
Homework may not be submitted through e-mail, no exceptions.
Due dates will be adjusted in Gradescope onlyas needed and the student is expected to check regularly for those adjustments. Due dates in D2L will not be updated.

Written homework is assigned regularly throughout the semester, for a total of approximately 80 problems. Two types of homework will be assigned:

Homework which consists of selected exercises in the required textbook.
Some custom homework will be composed by the instructor. Some of the custom problems will require programming.

Homework submission requirements

Using Gradescope for grading differs from other grading systems. Mainly, it uses AI to allow the instructor to accurately grade a larger number of problems than it would be possible otherwise. Some grading is completely automated (e.g., solutions to problems with a numerical answer). More comples answers may be grouped automatically by using Machine Learning, OCR and image analysis. However, it is possible to completely confuse the system by improperly structuring the submitted document. Therefore, please read the instructions below carefully and re-visit them as needed. Note that Gradescope supports automatic regrade requests which you can use if all fails.

The solutions must be structured in such a way that Gradescope can read them and that its 'AI' can interpret them. Your homework must be submitted as a PDF document, even if you use scanner or phone to capture images. Two typical workflows will be as follows:

Download the blank assignment (also called a 'template') from Gradescope.
Read and understand exactly what answers you need to provide. The space to enter the answer is a blue box, and marked with a label such as 'Q1.1' ("Question 1, part 1").
Work out the problem on "paper" (real or virtual), to obtain the answers. They must fit in the designated boxes in the 'template'. The size of the box is a hint from the instructor about the size of the answer (typically a number or a math formula) when entered by hand, using regular character size.
The recommended way to fill out the 'template' is paperless, by using suitable software and hardware (digital pen or tablet). I use a free program Xournal for this and it works great. You need to use it in combination with a digital pen or a tablet. It can produce a PDF easily, ready for submission to Gradescope.
You can also print the assignment on (real) paper, fill out the answers and scan the marked up document back to PDF format. However, the position of the boxes must be exactly (to a fraction of an inch) as in the original. Also, you may encounter a variety of "quality control" issues, especially if you are using a digital camera to scan the paper solution. All issues can be solved by a mix of the right hardware and software, but may not be the best time investment. The least troublesome way to scan is to use a real, flatbed scanner, e.g. in the library.
Upload the resulting document (a PDF of the 'template' marked up with your answers) to Gradescope. Your PDF must contain your name and student id in designated spaces. The Gradescope 'AI' will look for your name and student id, to properly associate it with your account.
After grading, the grade will be transmitted to D2L (Brightspace) and will be added to your 'Final Calculated Grade' automatically.
Do not reduce handwriting size! Reduce the size of your answer using
- closed form expressions;
- appropriate math functions, e.g., absolute value, min and max.
Under no circumstances write outside the provided space (boxes). Gradescope, and the grader only considers the content of the designated boxes.
IMPORTANT! Do not insert pages in the solution template. This will confuse Gradescope, and will result in reduced score and/or will require re-submission. However, you are encouraged to submit scratchwork. You should create pages at the end of the document. Similarly, if you run out of space in the template for your solution, you can continue the solution on a newly created page at the end of the document, adding a note in the template: "Solution continued on page 13" where page 13 will contain the continuation.

Programming and Software

The class will have small programming assignments. It is expected that you will be using software to gain insights into the assigned problems and subject matter. The programming assignments must be submitted in formats supported by Gradescope and the instructor. The number of programming languages will be limited two two or three. R will be supported and it is encouraged that you use it as it is most compatible with the course content.

For illustrating some aspects of the course, I will be using these programs (easy to download and free to use):

A computer algebra system (CAS) called Maxima.
The maxima GUI wxMaxima is a separate program and this is the preferred way to use Maxima if you are a beginner. During the previous semester students successfully applied Maxima to doing their homework, and I will provide examples of Maxima calculations in class.
The R programming language and environment, with a rich set of tools to do simulations in probability and stochastic processes (and analyze data).
The GUI (and more for R): RStudio. Makes use of R somewhat more pleasant, especially for a new user.

Final Examination

The final examination is scheduled for: May 8 (Wednesday), 1:00pm - 3:00pm.

The time, data and general exam rules are set by the University and can be found at these links:

Grading Scale and Policies

The student in the class normally receives a letter grade A, B, C, D or E.

The cut-offs for the grades are:

Grade	% Range
A	90%+
B	80-90%
C	70-80%
D	60-70%
E	0-60%

Normally, individual tests and assignments will not be "curved". However, grade cut-offs may be lowered at the end of the semester (but not raised!) to reflect the difficulty of the assignments and other factors that may cause abnormal grade distribution.

The grade will be computed by D2L and the partial grade will be updated automatically by the system as soon as the individual grades are recorded.

General UA policy regarding grades and grading systems is available at https://catalog.arizona.edu/policy-type/grade-policies

Safety on Campus and in the Classroom

For a list of emergency procedures for all types of incidents, please visit the website of the Critical Incident Response Team (CIRT):

https://cirt.arizona.edu/case-emergency/overview Also watch the video available at https://arizona.sabacloud.com/Saba/Web_spf/NA7P1PRD161/common/learningeventdetail/crtfy000000000003560

Classroom Behavior Policy

To foster a positive learning environment, students and instructors have a shared responsibility. We want a safe, welcoming and inclusive environment where all of us feel comfortable with each other and where we can challenge ourselves to succeed. To that end, our focus is on the tasks at hand and not on extraneous activities (i.e. texting, chatting, reading a newspaper, making phone calls, web surfing, etc).

Threatening Behavior Policy

The UA Threatening Behavior by Students Policy prohibits threats of physical harm to any member of the University community, including to one's self. See: http://policy.arizona.edu/education-and-student-affairs/threatening-behavior-students .

Accessibility and Accommodations

Our goal in this classroom is that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact Disability Resources (520-621-3268) to establish reasonable accommodations. For additional information on Disability Resources and reasonable accommodations, please visit http://drc.arizona.edu/ .

If you have reasonable accommodations, please plan to meet with me by appointment or during office hours to discuss accommodations and how my course requirements and activities may impact your ability to fully participate. Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable. Code of Academic Integrity Required language: Students are encouraged to share intellectual views and discuss freely the principles and applications of course materials. However, graded work/exercises must be the product of independent effort unless otherwise instructed. Students are expected to adhere to the UA Code of Academic Integrity as described in the UA General Catalog. See: http://deanofstudents.arizona.edu/academic-integrity/students/academic-integrity http://deanofstudents.arizona.edu/codeofacademicintegrity .

UA Nondiscrimination and Anti-harassment Policy

The University is committed to creating and maintaining an environment free of discrimination, http://policy.arizona.edu/human-resources/nondiscrimination-and-anti-harassment-policy . Our classroom is a place where everyone is encouraged to express well-formed opinions and their reasons for those opinions. We also want to create a tolerant and open environment where such opinions can be expressed without resorting to bullying or discrimination of others.

Additional Resources for Students

UA Academic policies and procedures are available at: http://catalog.arizona.edu/2015-16/policies/aaindex.html Student Assistance and Advocacy information is available at: http://deanofstudents.arizona.edu/student-assistance/students/student-assistance

Confidentiality of Student Records

http://www.registrar.arizona.edu/ferpa/default.htm .

Subject to Change Statement

Information contained in the course syllabus, other than the grade and absence policy, may be subject to change with advance notice, as deemed appropriate by the instructor.

Significant Dates (from the Registrar's Website)

Undergraduate

      

  
  
    Date
    Event
  
  
  
  
    January 10, 2024
    Classes Begin
  
  
    January 15, 2024
    Martin Luther King Jr. Holiday - No Classes
  
  
    March 2 - 10, 2024
    Spring Recess - No Classes
  
  
    May 1, 2024
    Last Day of Classes and Laboratory Sessions
  
  
    May 2, 2024
    Reading Day - No Classes or Finals
  
  
    May 3 - 9, 2024
    Final Examinations
  
  
    May 10, 2024
    Commencement
  
  
    May 10, 2024
    Degree Award Date for Students Completing by Close of Spring Semester
  






  Spring 2024 - Undergraduate Regular Academic Session
  
    
      
        Date
        Event
      
    
    
      
        10/1/2023
        Shopping Cart available
      
      
        1/9/2024
        Last day to file Undergraduate Leave of Absence
      
      
        1/9/2024
        Last day for students to add to or drop from a waitlist
      
      
        1/10/2024
        FIRST DAY OF SPRING CLASSES

            UAccess still available for registration

            First day to file for the Grade Replacement Opportunity (GRO)

            First day to add classes for audit and instructor signature is required
      
      
        1/15/2024
        Martin Luther King Day, no classes
      
      
        1/17/2024
        Last day to use UAccess for adding classes, changing classes, or changing sections
      
      
        1/18/2024
        Instructor approval required on a Change of Schedule form to ADD or CHANGE classes
      
      
        1/23/2024
        Last day to drop without a grade of W (withdraw)

            Classes dropped on or before this date will remain on your UAccess academic record with a status of dropped, but will not appear on your transcript

            Last day to change from credit to audit, or vice versa, with only an instructor's signature
      
      
        1/23/2024
        Last day for a refund
      
      
        1/24/2024
        Beginning today, students may completely withdraw from all classes in the term
      
      
        1/24/2024
        W period begins a penalty grade of W will be awarded for each withdrawal and the class(es) will appear on your transcript

            Beginning today, a change from credit to audit requires instructor approval on a Change of Schedule form
      
      
        2/1/2024
        Last day to apply for Spring degree candidacy without a late fee After this date a $50 00 Late Candidacy Application fee will be assessed
      
      
        2/6/2024
        Last day for department staff to add or drop in UAccess
      
      
        2/6/2024
        Last day to change from pass/fail to regular grading or vice versa with only instructor approval on a Change of Schedule form
      
      
        2/7/2024
        Instructor's and dean's signatures are required on a Change of Schedule form to change from pass/fail to regular grades or vice versa
      
      
        3/3/2024
        Last day to make registration changes without the dean's signature
      
      
        3/4/2024
        Instructor's and dean's signatures are required on all Change of Schedule forms to ADD or CHANGE classes
      
      
        3/4/2024
        Spring recess begins
      
      
        3/10/2024
        Spring recess ends
      
      
        3/26/2024
        Last day to file for Grade Replacement Opportunity (GRO)
      
      
        3/26/2024
        Last day for students to withdraw from a class online through UAccess

            Last day for students to change to/from audit with only instructor approval

            Last day for instructors to administratively drop students
      
      
        3/27/2024
        Instructor and dean's signatures required on a Late Change Petition in order to withdraw from class and students must have an extraordinary reason for approval

            Beginning today, a change from credit to audit will be permitted only if the student is doing passing work on the course. Instructor and dean's permission required on a Change of Schedule form
      
      
        4/9/2024
        Last day for students to submit a Late Change Petition to their college
      
      
        5/1/2024
        Last day to request a complete withdraw from all classes in the term
      
      
        5/1/2024
        Last day of class--no registration changes can be made after the last day of class
      
      
        5/2/2024
        Reading day, no classes
      
      
        5/3/2024
        Final exams begin
      
      
        5/9/2024
        Final exams end

            Final grades are available in UAccess as soon as the instructor posts them

            Per Faculty Senate Policy, grades should be submitted within two business days after the final exam
      
      
        5/10/2024
        Degree award date

Date	Event
January 10, 2024	Classes Begin
January 15, 2024	Martin Luther King Jr. Holiday - No Classes
March 2 - 10, 2024	Spring Recess - No Classes
May 1, 2024	Last Day of Classes and Laboratory Sessions
May 2, 2024	Reading Day - No Classes or Finals
May 3 - 9, 2024	Final Examinations
May 10, 2024	Commencement
May 10, 2024	Degree Award Date for Students Completing by Close of Spring Semester

Date	Event
10/1/2023	Shopping Cart available
1/9/2024	Last day to file Undergraduate Leave of Absence
1/9/2024	Last day for students to add to or drop from a waitlist
1/10/2024	FIRST DAY OF SPRING CLASSES UAccess still available for registration First day to file for the Grade Replacement Opportunity (GRO) First day to add classes for audit and instructor signature is required
1/15/2024	Martin Luther King Day, no classes
1/17/2024	Last day to use UAccess for adding classes, changing classes, or changing sections
1/18/2024	Instructor approval required on a Change of Schedule form to ADD or CHANGE classes
1/23/2024	Last day to drop without a grade of W (withdraw) Classes dropped on or before this date will remain on your UAccess academic record with a status of dropped, but will not appear on your transcript Last day to change from credit to audit, or vice versa, with only an instructor's signature
1/23/2024	Last day for a refund
1/24/2024	Beginning today, students may completely withdraw from all classes in the term
1/24/2024	W period begins a penalty grade of W will be awarded for each withdrawal and the class(es) will appear on your transcript Beginning today, a change from credit to audit requires instructor approval on a Change of Schedule form
2/1/2024	Last day to apply for Spring degree candidacy without a late fee After this date a $50 00 Late Candidacy Application fee will be assessed
2/6/2024	Last day for department staff to add or drop in UAccess
2/6/2024	Last day to change from pass/fail to regular grading or vice versa with only instructor approval on a Change of Schedule form
2/7/2024	Instructor's and dean's signatures are required on a Change of Schedule form to change from pass/fail to regular grades or vice versa
3/3/2024	Last day to make registration changes without the dean's signature
3/4/2024	Instructor's and dean's signatures are required on all Change of Schedule forms to ADD or CHANGE classes
3/4/2024	Spring recess begins
3/10/2024	Spring recess ends
3/26/2024	Last day to file for Grade Replacement Opportunity (GRO)
3/26/2024	Last day for students to withdraw from a class online through UAccess Last day for students to change to/from audit with only instructor approval Last day for instructors to administratively drop students
3/27/2024	Instructor and dean's signatures required on a Late Change Petition in order to withdraw from class and students must have an extraordinary reason for approval Beginning today, a change from credit to audit will be permitted only if the student is doing passing work on the course. Instructor and dean's permission required on a Change of Schedule form
4/9/2024	Last day for students to submit a Late Change Petition to their college
5/1/2024	Last day to request a complete withdraw from all classes in the term
5/1/2024	Last day of class--no registration changes can be made after the last day of class
5/2/2024	Reading day, no classes
5/3/2024	Final exams begin
5/9/2024	Final exams end Final grades are available in UAccess as soon as the instructor posts them Per Faculty Senate Policy, grades should be submitted within two business days after the final exam
5/10/2024	Degree award date

Material Covered

We will cover Chapters 7-10 of the book. Here is the approximate schedule with approximate dates when the particular sections shall be covered.

Chapter.Section	Title	Page	Covered	Date
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