PROBABILITY

MATH 336

FALL 2023

Professor Bradley A. Hartlaub
Office 305 Rutherford B. Hayes Hall
Phone 740-427-5405
e-mail hartlaub@kenyon.edu
Office Hours

Required Text

Learning Goals

Accessibility Accomodations

A student who thinks they may need an accommodation to access a campus program, activity, or service should contact Ruthann Daniel Harteis in Student Accessibility and Support Services (SASS) at danielharteis1@kenyon.edu  to discuss specific needs. Advance notice is required to review documentation, evaluate accommodation requests and provide notice or arrangements for any accommodation.

Title IX Responsibilities

As a member of the Kenyon College faculty, I am concerned about the well-being and development of students, and am available to discuss any concerns. However, I want you to know that faculty members are legally obligated to share certain information with the College’s Civil Rights & Title IX Coordinator. This requirement is to ensure your safety and welfare is being addressed. These disclosures include, but are not limited to: reports of discrimination or harassment due to a protected characteristic, including sexual harassment, sexual assault, relational/domestic violence, and stalking.

Homework

Homework assignments will be given throughout the semester. I encourage you to work on as many problems as possible, including problems which have not been assigned. Subsets of the homework assignments will be collected and graded. Your solutions must be submitted electronically to your Google Drive folder. You must submit a PDF of your solutions using a very specific naming structure. For example, the name of the file for the first homework assignment should be HW1-yourname.PDF. Working with other students is encouraged, but each student must submit her/his own solution for problems to be collected. For more infomation, see the departmental guidelines for collaboration on homework, which I expect you to follow.

Homework is due at the start of class on the assigned due date, unless specified otherwise. Each student will be allowed two "free" 48-hour extensions on homework assignments; no reason needs to be provided. Simply email me in advance of the due date to say that you would like to use one of your two extensions. After the second extension, late homework will not be accepted. However, your lowest homework score will be dropped at the end of the semester.

The grading rubric for all HW exercises is:

Complete (10/10)

Substantial (9/10)

Developing (8/10)

Developing (7/10)

Minimal (5/10 or 6/10)

No work or something completely off base (0/10)

Problem Sessions

During the semester we will have problem sessions which will be conducted by you (the students). These sessions are designed to improve your understanding of probability concepts and enhance your mathematical maturity by requiring a clear, detailed presentation of the material to your peers. During these sessions, you will be responsible for solving an assigned problem and presenting the solution to the rest of the class. Randomization will be used to assign at least two students to each exercise. Answering all questions about your solution is a required part of the presentation. Being able to solve problems and being able to present the solutions to a group in a logical and coherent fashion are two different tasks. Our goal is to master both tasks.

After your problem session presentation, you are required to upload a complete copy of your solution to the Google Drive folder !Problem Sessions - Student Solutions using a specific naming structure. For example, the name of the file for exercise 1.42 will be 1.42_yourname.PDF or 1.42_yourname.R or 1.42_yourname.RMD. The primary reason for the specific naming structure is so that the folder stays organized and the entire class has a complete set of solutions for every exercise that we discuss during our problem sessions.

Late Policy

Your work must be turned in before class begins on the assigned due date. No credit will be given for late papers, except in the two cases where you may opt to use your "free" 48-hour extension. If for any reason you cannot turn in your paper on the assigned date, you must contact me or send e-mail to hartlaub@kenyon.edu before class begins.

Exams

  • Exam 1 - Wednesday, October 4
  • Exam 2 - Friday, November 17
  • Comprehensive Final Exam - Friday, December 15, 1:30 - 4:30 pm

    • Group Projects

    Each group will prepare 20 minute presentations for class. You may use the blackboard, a standard overhead projector, Power Point, or some other presentation software of your choice.

    Your presentations will focus on probability topics of your choice. The topic should build on the basic foundation we have developed so far in the course, but the objective of this assignment is for you to apply the concepts and results we have learned to probability problems that goes beyond what we have covered in class. For example, you may want to introduce a new probability distribution (e.g., Cauchy, Logistic, Lognormal,Weibull, etc.) that we have not considered. You might want to look at the properties of this probability distribution (e.g., mean, variance, and moment generating function). You could also compare and contrast a probability model of your choice with the probability models we have studied.

    More details will be provided on our course web page as the project deadlines approach. However, a short proposal describing your project will be required. I will approve your project proposal or make suggestions as soon as possible after I receive your proposal. The proposal may be submitted via e-mail. Before your presentation, you should prepare a short (1 page, front and back if necessary) handout which summarizes the main ideas from your presentation for members of the audience. In short, I want you to be creative.

    We will have two sets of project presentations; one for discrete random variables and one for continuous random variables.

    Attendance Policy:

    In relation to the Kenyon Class Attendance Policy and The Department of Mathematics and Statistics Attendance Policy, nine class absences (whether excused or unexcused) will result in expulsion from the course.

    Grades

    Your course grade will be based on your overall percentage. The categories used to determine your overall percentage are listed below with their respective weights.
  • Homework Assignments (10%)
  • Problem Sessions and Activities (20%)
  • Projects (15%)
  • Exam 1(17.5%)
  • Exam 2 (17.5%)
  • Final Exam (20%)
    • Class participation will be used to help make borderline decisions.
    Course Outline
  • Chapter 1 First Principles
  • Chapter 2 Conditional Probability and Independence
  • Chapter 3 Introduction to Discrete Random Variables
  • Chapter 4 Expectation and More with Discrete Random Variables
  • Chapter 5 More Discrete Random Variables and Their Relationships
  • Chapter 6 Continuous Probability
  • Chapter 7 Continuous Distributions
  • Chapter 8 Densities of Functions of Random Variables
  • Chapter 9 Conditional Distribution, Expectation, and Variance
  • Chapter 10 Limits
  • Chapter 11 Beyond Random Walks and Markov Chains (if time permits)
  • Appendix D Working with Joint Distributions (if time permits)