PROBABILITY
MATH 336
FALL 2022
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 & Labs
Homework and lab assignments will be given weekly throughout the semester. You should work on as many problems as possible. This includes problems which have not been assigned. Your papers will be collected and graded frequently. All papers that you turn in must be legible with problem numbers and solutions clearly marked. I encourage you to discuss the concepts and problem solving techniques presented in class with other students. However, you must submit your own solution for each of the assigned problems to be collected. For more infomation, see the departmental guidelines for collaboration on homework, which I expect you to follow.Late Policy
Homework assignments must be turned in at the beginning of the class period on the assigned due date. No credit will be given for late papers. If for any reason you cannot turn in your paper on the assigned date, you must contact me before class. If you are unable to contact me, you can leave a message on my office phone (740-427-5405) or send e-mail to hartlaub@kenyon.edu.Problem Sessions
During the semester we will have weekly 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. 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.
Exams
Exam 1 - Wednesday, October 5 Exam 2 - Friday, November 18 Comprehensive Final Exam - Wednesday, December 14, 6:30 - 9:30 pm
Project
Each group will prepare a 20 minute presentation for class. You may use the blackboard, a standard overhead projector, Power Point, or some other presentation software for your presentation.
Your presentation will focus on a probability topic 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 a probability problem that goes beyond what we have covered in class. For example, you may want to introduce a probability distribution (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 the probability model of your choice with the probability models we have studied.
Another possible project could focus on different applications of some of the probability models we have studied. In short, I want you to be creative.
Project Deadlines:
- November 16, 2022 (or before) - a short project proposal describing your topic. 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.
- December 7, 2022 (or before) - 20 minute 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
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.Course OutlineClass participation will be used to help make borderline decisions.Homework Assignments (10%) Problem Sessions and Activities (20%) Project (10%) Exam 1(20%) Exam 2 (20%) Final Exam (20%)
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)