SYLLABUS: MATH 4530

PROBABILITY

SPRING 2021

Course overview

Instructor

Instructor: Kristina Wicke

Email address: [email protected]

Class Website: https://osu.instructure.com/courses/95901

Lectures: On CarmenZoom, MWF at 3:00-3:55pm (EDT/EST, Ohio Time Zone).

Office hours: Monday at 1:00-2:00pm and Friday at 1:00-2:00pm and by appointment (please schedule appointments at least 24 hours in advance). See the announcement about office hours on Carmen for the Zoom link.

Grader

Grader: tba

Email address: tba

Course Content and Goals

This is an introductory course in probability theory. Students will learn about probability spaces, discrete and continuous distributions and densities, expected values, functions of random variables and transformation techniques, joint distributions and independence. Students will also become familiar with the basic limit theorems in probability, including the law of large numbers and the central limit theorem. Along the way, students will learn how to interpret probabilistic statements, and will gain experience with solving introductory level and more challenging problems that involve randomness and chance.

Prerequisites: C- or better in MATH 2153, 2162.xx, 2173, 2177, 2182H, 4182H; or credit for 254.xx, 263.xx, 263.01H, or 264H.

Not open to students with credit for 5530H (531H), 530, or Stat 4201 (420).

Course materials

Required

Probability by Jim Pitman, 1993.

You can purchase the textbook from the bookstore or online, but an electronic copy is also available through the OSU library.

Supplemental References

Introduction to Probability by David F. Anderson, Timo Seppäläinen and Benedek Valkó, 2018.

John E. Freund’s Mathematical Statistics with Applications, Eighth Edition by Irwin Miller and Marylees Miller, 2014.

I will refer to these books, in addition to the required text, when creating course materials.

Moreover, Prof. Dr. David Sivakoff and Dr. Wasiur Rahman Khuda Bukhsh generously shared with me their teaching materials. I will use their material from time to time.

Course technology

For help with your password, university e-mail, Carmen, or any other technology issues, questions, or requests, contact the OSU IT Service Desk. Standard support hours are available at https://ocio.osu.edu/help/hours, and support for urgent issues is available 24x7.

•   Self-Service and Chat support: http://ocio.osu.edu/selfservice

•   Phone: 614-688-HELP (4357)

•   Email: [email protected]

•   TEL: 614-688-8743

Baseline technical skills necessary for online courses

•   Basic computer and web-browsing skills

•   Navigating Carmen

Technology skills necessary for this specific course

•   CarmenZoom

Necessary equipment

•   Computer: current Mac (OS X) or PC (Windows 10+) with high-speed internet connection

•   Webcam: built-in or external webcam, fully installed

•   Microphone: built-in laptop or tablet mic or external microphone

•   A scientific calculator. The one on your phone or computer is acceptable. You may also use a graphing calculator, but not one with a computer algebra system (CAS) for exams and quizzes.

Necessary software

•   You will need to have the ability to scan written work to upload certain assignments as PDF files through Carmen. There are a variety of free apps that can do this (search for “PDF scanner”). For instance, the Notes application that comes standard on an iPhone or iPad has this capability. Alternatively, you may use a tablet computer with a stylus to write your solutions using a handwriting app, then save them as a PDF file to upload to Carmen.

Course delivery

All lectures will be delivered as live CarmenZoom lectures at the scheduled class time (MWF 3:00-3:55pm EDT/EST). Lectures will be recorded and posted on the class website soon after. You will be responsible for watching any live content or recorded videos and studying the material that is assigned. In addition to lecture videos, assignments will be posted on the class website (Carmen). You will be given ample time to complete the assignments.

The instructor will hold weekly office hours via CarmenZoom. The dates and times will be announced later and posted on the Carmen website. The instructor will also initiate and manage active discussion boards, also via Carmen.

Apart from live lectures via CarmenZoom, most of the course can be completed asynchronously, meaning that you will have some flexibility to study materials and work on assessments according to your own daily schedule. In particular, all quizzes and exams will have a window of times during which you can start the assessment activity, and a fixed duration. For example, a quiz may be announced (in advance) for a Friday, so students would have a 24-hour window to start the quiz, and once the quiz is started it would need to be completed within the next 30 minutes (for instance – these parameters will depend on the assignment).

Grading and faculty response

Homework, Quizzes and Exams

Assignment or category	Percentage
Homework (Weekly)	15
Quizzes (Weekly)	15
Midterm Exam #1	20
Midterm Exam #2	20
Final Exam	30
Total	100

Homework

Homework assignments will be posted weekly on Carmen and will usually be due at 11:59pm on Mondays (unless it is a holiday). No late homework will be accepted. You are encouraged to work together on the homework, but do not copy any part of a homework. Each student must produce his/her own homework to be submitted electronically. Students are not permitted to look up or request solutions to homework problems in online forums or websites. All homework must be submitted online as a PDF file through the class website. Feel free to ask me for help during my office hours after you have made an attempt of the questions.

The grader for the course does not have the time to provide detailed explanations on each question that is graded. To make up for this, I will endeavor to create homework solutions that are detailed enough to allow you to understand how the question could be approached.

Homework preparation rules: Put your name and the homework assignment number on the top right corner of every page. Submit the problems in order. The purpose of the written homework is to assess and provide feedback on your understanding of and ability to explain the reasoning behind complex derivations or probabilistic arguments, which are difficult to assess via a Carmen quiz. Therefore, answers with little or no explanation or work shown will receive no credit. The lowest homework score will be dropped at the end of the semester.

Quizzes

There will be a weekly quiz on Fridays when there is not a midterm exam (with the exception of the first and last Friday in the semester). The quizzes will contain similar (but not identical) problems as the homework assignment due that week. It thus makes sense to revise the content of the homework due on Monday before taking the quiz on Friday. All quizzes will take place through the course website and you will have a 24-hour window to start the quiz. Once the quiz is started it will need to be completed within the next 30 minutes. The lowest quiz score will be dropped at the end of the semester.

Exams

There will be two midterm exams and one final exam (all exams will be administered remotely through the carmen course management system):

Midterm 1	Fri, Feb 19
Midterm 2	Fri, Mar 26
Final	Wed, Apr 28

All exams and quizzes are open book and open notes but must be completed alone. Use of any other materials are forbidden, including any websites or software packages. A calculator is allowed, but only one that does not have computational algebra capabilities.

The first midterm covers material up to and including Wed, Feb 17.

The second midterm covers material up to and including Wed, Mar 22.

The final will cover all the material for the course.

Full credit on short answer exam problems: You need to show justification for your work on each short answer exam problem. Answers without work will not receive full credit.

Grading

Homework will be marked out of 20 points each and quizzes will be marked out of 10 points each (in both cases the lowest score will be dropped), while exams will be marked out of 100 points; all scores will be converted into percentages. Final grades will be assigned based on the weighted averages of these percentages (15% for Homework, 15% for Quizzes, 20% for Midterm #1, 20% for Midterm #2, and 30% for Final Exam).

Grading Scale

93-100:	90-92.9999:	87-89.9999:	83-86.9999:	80-82.9999:	77-79.9999:	73-76.9999:	70-72.9999:	67-69.9999:	60-66.9999:	Below 60:
A	A-	B+	B	B-	C+	C	C-	D+	D	E

Late assignments and Makeup Exams

Late assignments will generally not be accepted, as the lowest homework and quiz scores will be dropped to account for missed assignments. If you cannot participate in the course for a prolonged period of time due to personal illness or family responsibilities due to illness, please contact me immediately to discuss options for completing work. 

If you absolutely need a makeup exam and have a valid excuse, please also contact me for the necessary arrangements. However, you must notify me in advance in such a situation. A make-up exam should be taken within a week of the missed exam. Exceptions to this policy will be permitted on a case-by-case basis and only in extreme situations.

Faculty feedback and response time

I am providing the following list to give you an idea of my intended availability throughout the course. (Remember that you can call 614-688-HELP at any time if you have a technical problem.)

Grading and feedback

For weekly homework, you can generally expect feedback within 7-10 days.

E-mail and Canvas Conversations

I will reply to e-mails and messages sent via Canvas Conversations within 24 hours on school days (Monday – Friday, excluding university holidays).

Discussion board

I will check and reply to messages in the discussion boards as appropriate every 24 hours on school days (Monday – Friday, excluding university holidays).

Live Zoom office hours

Each week, there will be live Zoom office hours. The dates and times of these will be communicated clearly and well in advance. An announcement will also be posted on the class website.

Attendance, participation, and discussions

Student participation requirements

Because this is a distance-education course, your attendance is based on your online activity and participation. The following is a summary of everyone's expected participation:

•   Live lectures: FLEXIBLE

Students will be expected to participate and ask questions in online live lectures. Live presentations will be recorded, so students can watch them later.

•   Office hours: OPTIONAL

All office hours are optional.

Discussion and communication guidelines

The following are my expectations for how we should communicate as a class. Above all, please remember to be respectful and thoughtful.

•   Writing style: While there is no need to participate in class discussions as if you were writing a research paper, you should remember to write using good grammar, spelling, and punctuation. Informality (including an occasional emoticon) is acceptable for nonacademic topics.

•   Tone and civility: Let's maintain a supportive learning community where everyone feels safe and where people can disagree amicably. Remember that sarcasm doesn't always come across online.

•   Citing your sources: When we have academic discussions, please cite your sources to back up what you say. (For the textbook or other course materials, list at least the title and page numbers. For online sources, include a link.)

•   Backing up your work: Consider composing your academic posts in a word processor, where you can save your work, and then copying into the Carmen discussion.

Other course policies

Health and safety

The Ohio State University Wexner Medical Center's Cornavirus Outbreak site (https://wexnermedical.osu.edu/features/coronavirus) includes the latest information about COVID-19 as well as guidance for students, faculty and staff. Guidelines and requirements for campus safety from the University’s COVID-19 Transition Task Force were published on July 1 on the Safe and Healthy website (https://safeandhealthy.osu.edu).

Student academic services

Student academic services offered on the OSU main campus http://advising.osu.edu/welcome.shtml.

Student support services

Student support services offered on the OSU main campus http://ssc.osu.edu.

Academic integrity policy

Policies for this online course

•   Assessments: You must complete the quizzes, midterm and final exams yourself, without any external help or communication. You may use only your textbook and notes, and a calculator that does NOT have a computer algebra system (CAS). Homework may be discussed with classmates, but submitted homework assignments should represent your own efforts. DO NOT use websites to look up (or request) solutions to problems. Paraphrasing a solution that is not your own still constitutes plagiarism.

•   Reusing past work: In general, you are prohibited in university courses from turning in work from a past class to your current class, even if you modify it.

Ohio State’s academic integrity policy

It is the responsibility of the Committee on Academic Misconduct to investigate or establish procedures for the investigation of all reported cases of student academic misconduct. The term “academic misconduct” includes all forms of student academic misconduct wherever committed; illustrated by, but not limited to, cases of plagiarism and dishonest practices in connection with examinations. Instructors shall report all instances of alleged academic misconduct to the committee (Faculty Rule 3335-5-487). For additional information, see the Code of Student Conduct http://studentlife.osu.edu/csc/.

Copyright disclaimer

The materials used in connection with this course may be subject to copyright protection and are only for the use of students officially enrolled in the course for the educational purposes associated with the course. Copyright law must be considered before copying, retaining, or disseminating materials outside of the course.

Please do not disseminate any course materials, including lecture videos, assignments, and solutions outside of the course.

Statement on title IX (Recommended)

Title IX makes it clear that violence and harassment based on sex and gender are Civil Rights offenses subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories (e.g., race). If you or someone you know has been sexually harassed or assaulted, you may find the appropriate resources at http://titleix.osu.edu or by contacting the Ohio State Title IX Coordinator, Kellie Brennan, at [email protected]

Accessibility accommodations for students with disabilities

The university strives to make all learning experiences as accessible as possible. In light of the current pandemic, students seeking to request COVID-related accommodations may do so through the university’s request process, managed by Student Life Disability Services. If you anticipate or experience academic barriers based on your disability (including mental health, chronic, or temporary medical conditions), please let me know immediately so that we can privately discuss options. To establish reasonable accommodations, I may request that you register with Student Life Disability Services. After registration, make arrangements with me as soon as possible to discuss your accommodations so that they may be implemented in a timely fashion. SLDS contact information: [email protected]; 614-292-3307; http://slds.osu.edu; 098 Baker Hall, 113 W. 12th Avenue.

Accessibility of course technology

This online course requires use of Carmen (Ohio State's learning management system) and other online communication and multimedia tools. If you need additional services to use these technologies, please request accommodations with your instructor.

•   Carmen (Canvas) accessibility

•   Streaming audio and video

•   Synchronous course tools

Your mental health

As a student you may experience a range of issues that can cause barriers to learning, such as strained relationships, increased anxiety, alcohol/drug problems, feeling down, difficulty concentrating and/or lack of motivation. These mental health concerns or stressful events may lead to diminished academic performance or reduce a student’s ability to participate in daily activities. The Ohio State University offers services to assist you with addressing these and other concerns you may be experiencing. If you or someone you know are suffering from any of the aforementioned conditions, you can learn more about the broad range of confidential mental health services available on campus via the Office of Student Life’s Counseling and Consultation Service (CCS) by visiting ccs.osu.edu or calling 614- 292-5766. CCS is located on the 4th Floor of the Younkin Success Center and 10th Floor of Lincoln Tower. You can reach an on call counselor when CCS is closed at 614-292-5766 and 24 hour emergency help is also available through the 24/7 National Suicide Prevention Hotline at 1-800-273- TALK or at suicidepreventionlifeline.org 

Disclaimer

This syllabus should be taken as a fairly reliable guide for the course content. However, you cannot claim any rights from it and in particular I reserve the right to change due dates or the methods of grading and/or assessment if necessary. Any changes will be communicated to you through official course announcements.

Course schedule (tentative)

Week	Dates	Topics (sections in textbook, roughly)
1	Jan 11, 13, 15	Equally likely outcomes & Interpretations (1.1-1.2), Distributions (1.3) Conditional Probability and Independence (1.4)
2	Jan 20, 22 (no class on Jan 18)	Bayes’ Rule (1.5) Sequences of Events (1.6) Quiz 1 on Jan 22
3	Jan 25, 27, 29	Sequences of Events cont. (1.6) Binomial Distribution (2.1) Random Sampling (2.5) Quiz 2 on Jan 29
4	Feb 1, 3, 5	Random Variables (3.1) Expectation (3.2) Quiz 3 on Feb 5
5	Feb 8, 10, 12	Expectation cont. (3.2) Standard Deviation and Normal Approximation (2.2 and 3.3) Quiz 4 on Feb 12
6	Feb 15, 17, 19	Standard Deviation and Normal Approximation cont. (2.2 and 3.3) Review I Midterm 1 on Feb 19
7	Feb 22, 26 (no class on Feb 24)	Discrete Distributions (3.4) Quiz 5 on Feb 26
8	Mar 1, 3, 5	Poisson Distribution and Poisson Approximation (2.4 and 3.5) Probability Densities (4.1) Quiz 6 on Mar 5
9	Mar 8, 10, 12	Exponential and Gamma Distributions (4.2) Change of Variable (4.4) Cumulative Distribution Functions (4.5) Quiz 7 on Mar 12
10	Mar 15, 17, 19	Moment generating functions Uniform Distributions (5.1) Densities (5.2) Quiz 8 on Mar 19
11	Mar 22, 24, 26	Independent Normal Variables (5.3) Review II Midterm 2 on Mar 26
12	Mar 29, Apr 2 (no class on Mar 31)	Operations (5.4) Quiz 9 on Apr 2
13	Apr 5, 7, 9	Conditional Distributions: Discrete Case (6.1) Conditional Expectation: Discrete Case (6.2) Conditioning: Density Case (6.3) Quiz 10 on Apr 9
14	Apr 12, 14, 16	Covariance and Correlation (6.4) Bivariate Normal (6.5) Quiz 11 on Apr 10
15	Apr 19, 21, 23	Chi-Square distributions t- and F-distributions Final Review

Final exam is on April 28.