Introduction to Probability Theory | Math M463 | Section 1489

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Instructor Contact Information

Instructor: Nayeong Kong, Ph.D.

• Phone: 765-973-8677
• Office: Whitewater 200B
• Office Hours: Thursday, 5:00 PM EST. Saturday by appointments

Communication Policy

Canvas messaging is my preferred means of contact.  I will return your messages and e-mails within 48 business hours.  In case of emergency only email me at kongna@iu.edu

 

Course Description and Structure

This course is designed to introduce students to various topics in probability and uncertainty that they will encounter in economic theory. The concepts are illustrated with actual examples from the economics literature. Exercises are designed to encourage the student to begin thinking about probability.

The M463 class is entirely online, with a focus on covering multiple sections of the textbook each week. As a student, it is your responsibility to find time to watch the Lecture Videos and take notes, as if you were attending an in-person class. While reviewing the lecture videos and textbook, pay close attention to the definitions and proof techniques discussed. Then, attempt the homework problems and engage in discussion with your classmates and instructor in the designated forum. It is important to note that most assignment problems are related to proofs, so avoid trying to imitate a similar problem and instead focus on learning how to apply proof techniques in a new setting. Before attempting any homework problems, make sure to thoroughly review the book and lecture videos. Then, carefully read each homework problem to gain a full understanding before generating ideas based on what you have learned from the course material.

In the field of mathematics, we develop various tools, strategies, proof techniques, definitions, and theorems to help us prove new statements. When solving a problem, we must carefully use and combine some or all of these pieces in a logical way. The primary goal of this course is to train you to establish mathematical results rigorously.

 

Prerequisites & Necessary Skills

The prerequisite courses for M463 are M301 or M303, and M311.

 

Required Computer & Digital Literacy Skills

• Comfort using Canvas, sending email with attachments, downloading and installing software, and using video conferencing tools like Zoom.
• Proficiency using Microsoft Office programs like Word, PowerPoint, and Excel.
• Proficiency using any Internet Service Provider (ISP), Microsoft Office 2010 or higher or Office 365, Mozilla Firefox 13.0 or higher or Google Chrome, Adobe Reader 

 

Required Texts and Materials

You have one textbook assigned for this course:

Introduction to probability 1st Edition by David F. Anderson, Timo Seppalainen, Benedek Valko (ISBN: 9781108415859)

Reading a textbook is an essential part of every course. Textbooks offer information on concepts, ideas, terms, and other material necessary to understanding this course of study. You are expected to read the material in the textbook before watching the videos.

In this course, I use modules as a way to structure and organize the course. Each module is designed around a particular part of the course. Each module contains the learning objectives for that particular module and is divided into specific subsections. In each subsection, you will find supplemental materials to help you learn the important ideas/concepts related to that part of the course. Like lectures in a traditional classroom, the material you find in the modules is there to help simplify and clarify important points you find in the textbook. Here you will have access to videos, websites, and other materials chosen to help you better understand the course material. As with the textbook, this material gives you a broader view of the material we are covering in this course. There are no optional course materials and learning activities in the course. You are expected to go through all the material to complete this course.

 

Course Learning Outcomes

At the end of this course, students will be able to:

CLO 1: Specify the basic probability axioms and rules to evaluate probabilities of common named discrete random variables.

CLO 2: Authenticate the probability density function of transformations of random variable.

CLO 3: Select appropriate probability distributions (Gaussian and Poisson) to approximate probabilities of binomial events.

CLO 4: Verify the marginal and joint distributions of bivariate random variables.

CLO 5: Evaluate the distribution of the sum of two discrete or continuous random variables using convolution.

CLO 6: Select appropriate probability concepts and specific measures in statistical analysis.

In addition to the course learning outcomes, each module has its own learning outcomes. Each module outcome aligns with the larger course outcomes. These will be annotated with a CLO designation after each outcome. These are located at the beginning of each module.

 

Campus Learning Outcomes

The content of this course also aligns with the following IUE Campus Learning Outcomes

• Communicate clearly and effectively in written and oral forms.
• Access, use and critically evaluate a variety of relevant information sources.
• Apply principles of inquiry to define and analyze complex problems through reasoning and discovery.
• Demonstrate a deep understanding of field of study.
• Demonstrate the ability to relate within a multicultural and digitally connected world.

 

Technical Requirements

To participate in an online course, you will need a newer model (Windows or Macintosh) computer, a recent version of at least two web browsers, a 'high-speed' internet connection (does not have to be in the home) and basic computer skills. A student may have to access and/or download large class files. The following is the suggested minimum computer system requirements:

• Hardware Requirements for Laptop and Desktop
  • Windows 7 or Macintosh OS X ( (10.7 - Lion) or higher Operating System
  • CPU (Processor) speed of 2.4 GHz or faster
  • 4 gigabyte (GB) RAM (1 dimm recommended)
  • 20 GB available hard disk space (Storage)
  • High speed Internet access (cable, DSL, etc.)
• Computer software requirements:
  • Any Internet Service Provider (ISP)
  • Microsoft Office 2010 or higher* or Office 365
  • Mozilla Firefox 13.0 or higher and/or Google Chrome
  • Adobe (Acrobat) Reader [http://get.adobe.com/reader/]
• Guidelines for Mobile Technology
  • Camera: 2.0 M Pixel Camera (or higher)
  • Web conferencing ability (such as Facetime or Skype)
• Wireless: WLAN 802.11 b/g/n@2.4GHz and/or Bluetooth V3.0 (or higher)
• CPU (Processor) speed of1 GHz or faster
• 16 GB available hard disk space (Storage) at minimum
• Compatible with iPad 2 Apps Recommended.

 

Technical Support

You will participate in this course using the IU Canvas platform. Once you are on the platform, you can learn how to use Canvas effectively by clicking the “Help” link on the top right of the course page on Canvas. In addition, the IU Knowledge Base is a good resource for any technical questions you may have. 

Contact the IT Help Desk at iueitsup@indiana.edu or by calling 765-973-8375. Most problems can be resolved in less than 24 hours. If there is a system-wide service problem, you will receive email notices regarding the problems and their resolution.

 

Course Technology Accessibility Statements and Privacy Policies

Accessibility Statements

Your accessibility needs are also important to us. Below are link to the accessibility statements for the tools we will be using in this course.

Youtube Accessibility: https://support.google.com/youtube/answer/189278?hl=en

Canvas Accessibility: https://community.canvaslms.com/t5/Accessibility/bg-p/accessibilityblog-board

Adobe Accessibility: https://www.adobe.com/accessibility.html

 

Privacy Policies

IU East cares about protecting your privacy. Below are the privacy policies for tools we will be using in this course.

Adobe Privacy Policy: https://www.adobe.com/privacy/policy.html

Canvas Privacy Policy: https://www.instructure.com/policies/privacy

Youtube Privacy Policy: https://support.google.com/youtube/answer/2801895?hl=en

 

Course Assessment & Grades

Course Assessment:

There are two types of assessment: Formative and summative. Formative assessment is for you to determine whether you are learning the material; essentially formative assessment consists of practice questions. There are no grades attached to formative assessment. You will notice that there are questions on the narrated slides built into this course to assist you in studying; there are also questions in your xxx. These questions are not graded; only you will know how well you did on these or whether you decided to skip them. I encourage you to complete all of the formative assessment to ensure the highest possible grade on your summative assessment. Summative assessment is graded. There are multiple summative assignments in this course.

You will be graded in four (4) ways: Attendance, Assignments, Discussions, and Exams. Grades will be posted on Gradebook. Please submit all work through Canvas; do not send anything to my email address for grading.

• Attendance: 
  • You have to attend three(or more) office hour sessions this semester. (This will be counted as 5% among the overall scores.)
  • If you cannot attend online office hour sessions due to your regular work schedule, you should contact me in the first week of the semester.

 

• Assignments: Homework assignments allow you to explore certain topics and apply the material you learn from the textbook. Specific directions for each assignment will be located in modules. All homework assignments will contribute 30% of the total course grade. If necessary, you should start each single homework problem on a separate page. Leave enough space so that I can quickly write comments during grading. We will complete each problem in multiple stages. You will need ample space, and you should be prepared to erase or cross out attempts that did not work. When creating proof, it is prevalent to determine (after writing a few paragraphs) that the effort you chose does not work and that a new attempt is required. Beginning with multiple attempts is not an indication of a lack of knowledge; it is part of the learning process.
  • Submitting Assignments: 

    You need to either type your homework in Word/Latex or scan neatly handwritten work and submit it as one single pdf file even multiple sections are covered. DO NOT upload multiple files for one assignment. Otherwise, I may grade the last submission and fail to grade the previous submissions.

    Please ALWAYS SUBMIT A PDF FILE because Canvas is compatible with pdf and may turn some characters in a non-pdf file into something weird.

    Please note that your assignment must be legible. Write neatly, or type! Typing may seem cumbersome, and it is even not a mandatory part of the course, but it helps you revise a document reasonably easy way without rewriting everything. Moreover, by typing your assignments, you will develop your math typing skill, which will be very helpful in math writing if you concentrate on mathematics in the future and easily manage multiple files you create throughout the semester.
  • Late Homeworks
    An assignment must be submitted before the deadline. If you miss the homework deadline, you will lose 20% of the total grade until one week, and I WILL NOT accept late homework for more than one week. This is non-negotiable except in special unavoidable circumstances such as when you are sick and provide me a doctor's note or when you have been affected by harsh weather conditions and provide convincing evidence etc., for the missed deadline.

 

• Online Discussions: 

  It would help if you discussed all questions related to examples, exercises, and difficulties in any topic in the lectures and textbook, assignments such as homework, group projects, exams, and other technical issues in the discussion forum in Canvas. The discussion forum is a primary platform for students' engagement to get help from instructors and peers. Participation in the discussion forum is mandatory and is a significant part of your overall course grade.

  You may contribute in two ways: either by asking an informed question or by helping with someone else's question (NEVER answer fully, share some ideas!). Your participation is considered to be more significant if you do not limit yourself in only asking questions but also equally ask questions and answer other's questions. Your post cannot be generic or something that can be copied from somewhere, so use it sparingly. NO CREDIT will be given for just asking a question without sharing what you tried to do and where you had a problem.

  You need to post a minimum of THREE times substantially in a weekly discussion forum. Those posts must come on two or more different days of that week. A response to someone's posting is considered to be SUBSTANTIAL if it delivers conceptual mathematical ideas and insights.

  • Not Substantial:
    • I don't get it! (Not specific)
    • What is the due date of homework 7? (Not on topic)
    • Look the page 35 in the book. (Not specific)
    • Thank you! I understand it now! (Not specific)
  • Substantial:
    • Could you explain the definition of one-to-one correspondence function? (A specific question on topic)
    • One to one correspondence means that the function is one to one and onto (A specific answer)
    •  So you mean that a function f : A -> B is a one-to-one correspondence is a one-to-one and onto. (A summary of the previous answer).

 

• Exams (Midterm and Final): There will be one Midterm Exam and one Final Exam. The mid-term and final exams will be open books and open notes. You have to complete and upload the midterm within 24 hours and the final exam within 36 hours from the time you open the exam. You will be given instructions on where to download/upload the exams. Problems on the exam will be similar to those in homework and quizzes.

 

How Will I Know How I’m Doing in This Course?

Success in this course will require the following:

• Doing all assignments. Watching lecture videos and paying attention and participating in the Discussion Sessions.
• Study, study, study! For every hour of this course (in this case, a 3-hour course) you should be spending at least 2-3 hours a week outside the classroom.  So, in addition to attending class, you should be spending at the very least an additional 6-9 hours a week outside the classroom to do well in this course. 
• If you ever have any questions and/or concerns, please contact me as soon as possible. I am here to help you out any way I can.

Grade Distribution:

 

Weekly Assignments	11*13.64 points = 150 points	30%
Online Discussion	11 * 4.54 points = 50 points	10%
Midterm Exam	100 points	20%
Final Exam	200 points	40%
Total	500 points	100%

 

 

Grading Scale

 

Grade	Equivalent Percentage
A+	>=97.00%
A	93.00 - 96.99%
A-	90.00 - 92.99%
B+	87.00 - 89.99%
B	83.00 - 86.99%
B-	80.00 - 82.99%
C+	77.00 - 79.99%
C	73.00 - 76.99%
C-	70.00 - 72.99%
D+	67.00 - 69.99%
D	60.00 - 66.99%
F	<=59.99%

Note: If you are on track for a D, you are failing the course.

 

Late Work

An assignment must be submitted before the deadline. If you miss the homework deadline, you will lose 20% of the total grade until one week, and I WILL NOT accept late homework for more than one week. This is non-negotiable except in special unavoidable circumstances such as when you are sick and provide me a doctor's note or when you have been affected by harsh weather conditions and provide convincing evidence etc., for the missed deadline.

 

Academic Support Services

IU East offers a variety of services to assist you in your academic endeavors. This includes everything from advising for your courses to student counseling support. You can find a list of our students' academic support and student services at the Student Success Hub. You can either click on the link or click on the tab named "Student Success Hub" found to your left in Canvas.

 

University Policies

Accommodations

Indiana University East Students may not be denied access to the benefits of an education per the American Disabilities Act (ADA). If you require academic assistance for a disability, please contact the Office of Disability Services (Hayes Hall 064, 765-973-8446) to establish your eligibility for accommodations. Once these have been authorized, please make an appointment with your instructor to review how the accommodation will be provided in your class. For more information, you can also visit the following website: https://www.iue.edu/disability/services.php

 

Intellectual Dishonesty

Academic honesty is fundamental to the activities and principles of this university.  All academic community members must be confident that each person’s work has been responsibly and honorably acquired, developed, and presented.  Any effort to gain an advantage not given to all students is dishonest whether the action is successful. In the context of this course, this means that you are not permitted to let anyone else access Canvas or MyMathLab with your login credentials and that you will not seek help from anyone (including the internet) while you are taking a quiz or a test. Please understand that the penalty for cheating on courses may be a failing grade for this course, probation, suspension, or even expulsion from the university.

 

Title IX Sexual Misconduct

The University does not tolerate acts of sexual misconduct, including sexual violence. If you have experienced sexual violence or know someone who has, the University can help. It is important to understand that federal regulations and University policy require faculty to immediately report complaints of sexual misconduct known to them to the University Title IX Coordinator or the Deputy Title IX Coordinator to ensure that appropriate measures are taken. Resources are made available.

Those individuals will work with you to protect your privacy by sharing information with only those with legitimate administrative or legal reasons to know. If you are seeking help and would like to speak to someone confidentially or to learn more about campus resources, you can find more information at http://stopsexualviolence.iu.edu/."

 

Code of Student Rights, Responsibilities, and Conduct

Students are expected to adhere to the Code of Student Rights, Responsibilities, and Conduct at all times. Any inappropriate behavior, disruptive conduct (e.g., engaging in hostile or disrespectful commentary on the site, or discussing irrelevant evidence) or non-compliance with faculty directions can result in a charge of Academic and/or Personal Misconduct, the consequence of which could be a variety of sanctions either from the instructor or the Dean of Students. For more information see The Code of Student Rights, Responsibilities, and Conduct.

 

University Policies:

 

• Classroom Etiquette

 

In all courses, students should respect one another and their ideas. In this course, I expect you all to be considerate in your communications and discussions with others. It does not mean you have to agree with those you work with, but you should be respectful and thoughtful about how you talk with others. The tone is sometimes lost in online communications, so be sure to be thoughtful in the way your communications might come across to others. Be professional and respectful in all your communications in this course.

 

• Academic Support and Student Services

 

IU East offers a variety of services to assist you in your academic endeavors. This includes everything from advising for your courses to student counseling support. You can find a list of our students' academic support and student services at the Student Success Hub. You can either click on the link or click on the tab named "Student Success Hub" found to your left in Canvas.

 

• Students with Disabilities

 

Indiana University East Students may not be denied access to the benefits of an education per the American Disabilities Act (ADA). If you require academic assistance for a disability, please contact the Office of Disability Services (Hayes Hall 064, 765-973-8446) to establish your eligibility for accommodations. Once these have been authorized, please make an appointment with your instructor to review how the accommodation will be provided in your class. For more information, you can also visit the following website: https://www.iue.edu/disability/services.php

 

 

• Honesty Statement

 

Academic honesty is fundamental to the activities and principles of this university.  All academic community members must be confident that each person’s work has been responsibly and honorably acquired, developed, and presented.  Any effort to gain an advantage not given to all students is dishonest whether the action is successful. In the context of this course, this means that you are not permitted to let anyone else access Canvas or MyMathLab with your login credentials and that you will not seek help from anyone (including the internet) while you are taking a quiz or a test. Please understand that the penalty for cheating on courses may be a failing grade for this course, probation, suspension, or even expulsion from the university.

 

• Course Withdrawal

 

Circumstances sometimes arise, requiring the student to withdraw from the course. Failure to continue class attendance does not constitute withdrawal and will result in a grade of F in the course. March 13th is the deadline to drop or withdraw from the course with an automatic “W.” After this date, the instructor must approve all withdrawals. To receive a “W” after the deadline, the student must pass the class at the request time. Otherwise, the grade is posted as an “F.” (See the full “Drop/Add” policy on the “Campus Course Policies” link, available on the left tab of your courses in Canvas)

 

Course Withdrawal Procedures

During the first week of classes you may drop a class with no grade recorded on your transcript. From the second week of classes through the ninth week (the ‘auto W’ period), you may withdraw from a class with an automatic grade of ‘W’. This will be recorded on your transcript, but not included in your GPA.

 

After the 'auto W' period, a student wishing to withdraw with a grade of 'W' must be passing the course at that time. You must complete a 'Drop Only' form and contact the offices listed for signatures before giving the form to the instructor. The instructor will confirm on the form that you are passing at that time for a 'W' grade or that your grade is an 'F.' This 'F' grade WILL affect your GPA.

 

• Incomplete Grades

 

The grade of "I" (Incomplete) may be given to a student whose work in a course is satisfactory except that some terminal aspect of the course requirements has not been completed. The grade "I" will only be given if the instructor has sufficient reason to believe that failure to satisfy the course requirements was beyond the student's control and that it would be unjust to hold the student to the time limits usually fixed for completion of the required work.

 

• Grade Appeals

 

If you believe the grade received in a course is incorrect, you should follow the Grade Appeal Policy. The initial appeals process states that “Students who are dissatisfied with the grade received in a course should contact the instructor and attempt to resolve the matter amicably and informally. If the matter cannot be resolved, the student should consult the IU East Grade Appeal Policy and follow the procedures stated therein.”

 

*For full IU East Grades and Grading Policies: http://www.iue.edu/registrar/policies/grading_policy.php

 

• Sexual Misconduct

 

The University does not tolerate acts of sexual misconduct, including sexual violence. If you have experienced sexual violence or know someone who has, the University can help. It is important to understand that federal regulations and University policy require faculty to immediately report complaints of sexual misconduct known to them to the University Title IX Coordinator or the Deputy Title IX Coordinator to ensure that appropriate measures are taken. Resources are made available.

 

Those individuals will work with you to protect your privacy by sharing information with only those with legitimate administrative or legal reasons to know. If you are seeking help and would like to speak to someone confidentially or to learn more about campus resources, you can find more information at http://stopsexualviolence.iu.edu/."

• Responsible Employees

All IUE Faculty are considered Responsible Employees for purposes of IU policy.This means we have an obligation to report incidents of possible discrimination, harassment, and/or sexual misconduct known to us to our Deputy Sexual Misconduct & Title IX Coordinator:  Tracy Amyx,Whitewater Hall 101K, 765-973-8402, trramyx@iue.edu.     

As you might remember, we are also required to complete Responsible Employee training each year. You will receive an email letting you know when that training is available.

The statement for syllabi that follows, helps students understand our obligations to them, and informs them of their rights and available support resources on campus.  By including this statement, we are providing students easy and private access to information regarding resources and reporting options if they or someone they know has experienced discrimination, harassment, and/or sexual misconduct, as well as information on bias reports or requesting an ADA accommodation.

• INDIANA UNIVERSITY POLICY ON DISCRIMINATION, HARASSMENT, AND SEXUAL MISCONDUCT:

As your instructor, one of my responsibilities is to create a positive learning environment for all students. IU policy prohibits sexual misconduct in any form, including sexual harassment, sexual assault, stalking, sexual exploitation, and dating and domestic violence.  If you have experienced sexual misconduct, or know someone who has, the University can help. If you are seeking help and would like to speak to someone confidentially, you can make an appointment with Jennifer Claypoole, Director of Mental Health – 765-973-8646.

It is also important that you know that because of my role, University policy requires me to share information brought to my attention about potential sexual misconduct with the campus Deputy Sexual Misconduct & Title IX Coordinator or the University Sexual Misconduct & Title IX Coordinator.  In that event, those individuals will work to ensure that appropriate measures are taken and resources are made available. Protecting student privacy is of utmost concern, and information will only be shared with those that need to know to ensure the University can respond and assist.  I encourage you to visit stopsexualviolence.iu.edu to learn more.

Indiana University also prohibits discrimination on the basis of age, color, disability, ethnicity, sex, gender identity, gender expression, genetic information, marital status, national origin, race, religion, sexual orientation, or veteran status.

If you feel like you have experienced discrimination, harassment, or sexual misconduct and wish to make a report, please contact Tracy Amyx, Interim Deputy Sexual Misconduct and Title IX Coordinator – trramyx@iue.edu – 765-973-8402 or make a report through the online reporting form here.

 

• BIAS INCIDENT REPORTING

Indiana University is committed to creating welcoming, inclusive, and respectful campus communities where everyone can thrive and do their best work—a place where all are treated with civility and respect. If you experience or witness an incident of bias, you should report it.  For more information, see Bias Incident Reporting. 

 

• ACCESSIBILITY & ACCOMMODATIONS

Indiana University is dedicated to ensuring that students with disabilities have the support services and reasonable accommodations needed to provide equal access to academic programs. To request an accommodation, you must establish your eligibility by working with Accessible Educational Services (AES) on your campus - asiue@iue.edu . Additional information can be found at accessibility.iu.edu. Note that services are confidential, may take time to put into place, and are not retroactive; captions and alternate media for print materials may take three or more weeks to get produced. Please contact your campus AES office as soon as possible if accommodations are needed.

Mental Health:

IU East offers free counseling services to all students on campus. The Counseling office is located in WZ 116A. The services range from one-on-one sessions with an IU East licensed clinical professional to group support sessions. The sessions are typically 1 hour long and can be done in person or through a secure zoom call. You must be present in the state of Indiana during the Zoom call. Students are offered up to six free sessions per semester. If you are seeking help, appointments can be made at 765-973-8646. To schedule an appointment online or find resources if you are struggling in any way, please visit this page https://www.iue.edu/healthy/mind/

 

• Basic needs security:
  Any students who face challenges securing their food or housing and believes this may affect their performance in the course should contact the Dean of Students Amy Jarecki (phone number: 765-973-8525) for support. Additionally, IU East employs a student advocate (phone number: 765-973-8395), to help. Furthermore, please notify me if you are comfortable in doing so. This will enable me to provide any resources that I may possess.

 

• Academic support and student services:
  IU East offers a variety of services to assist you in your academic endeavors. This includes everything from advising for your courses to student counseling support. A list of the academic support and student services offered for our students can be found  

 

• Honesty statement:
  Academic honesty is fundamental to the activities and principles of this university.  All members of the academic community must be confident that each person’s work has been responsibly and honorably acquired, developed and presented.  Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful.  All submitted written work is to be done by the student her/himself.  The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from reduction in grade, probation to expulsion.  Using someone else’s work as if it is your own— plagiarism— is a serious university offense and will be dealt with following university guidelines.  You must cite borrowed ideas or text, including lecture material, regardless of whether it is a direct quote or a paraphrasing.  When in doubt— cite. (See section III, Student Misconduct, of the Code of Student Rights, Responsibilities, and Conduct, available on the “Campus Course Policies” link, available on the left tab of your courses in Canvas).