Math 3090 – Mathematical Probability

Lecture Time: 12:00pm
  1:50pm (MW) Location: Knudson Hall 301 (M), Zoom (W)

Textbook: Ross, A First Course in Probability 9th Ed.

Prerequisite: Math 2080 and Math 3080

Instructor: Mei Yin
Office and Office Hours: Zoom, 3:30pm  5:00pm (MW), or by appointment

Lecture Schedule: Here is a plan of the course (may be altered for pedagogical reasons as the course develops).

Ch. 6: Jointly Distributed Random Variables
2 weeks
Ch. 7: Properties of Expectation
5 weeks
Ch. 8: Limit Theorems
2 weeks
Project Presentation
1 week

Course Description: Topics of study will include limit theorems for independent random variables, multivariate distributions, and generating functions.

Learning Objectives: By the end of the course, a student should be able to:
1. Develop an understanding for continuous and discrete multivariate probability distributions and their fundamental properties.
2. Compute the expected value and variance of multivariate distributions, and apply the knowledge in real-life situations.
3. Know basic limit theorems in probability and their applications.

Tentative Calendar:

The Week Of
Material Covered
January 11  January 15
Introduction, 6.1, 6.2, 6.3
January 19  January 22
6.4, 6.5
January 25  January 29
6.7, 7.1, 7.2
February 1  February 5
7.3, 7.4, 7.5
February 8  February 12
7.6, Review
February 15 – February 19
Midterm, 7.7
February 22  February 26
7.8, 7.9, 8.1
March 1 March 5
8.2, 8.3, 8.4
March 8  March 12
8.5, 8.6
March 15  March 19
Project Presentation

Grading: Your final grade for the course will be determined based on a numerical weighted average calculated as follows: Homework 30% Midterm 30% Final Project 40%. This average percentage will then be converted into a final letter grade based partially on how other students perform this quarter, and partially on typical percentage grades from previous quarters of the course.

Homework will be assigned about once a week. All communication will be paperless. Homework should be turned in via Canvas and the due date is every Monday at the beginning of the class. Homework that is turned in on Tuesday (i.e. one day late) will be graded with 25% penalty. Homework that is turned in on Wednesday (i.e. two days late) will be graded with 50% penalty. Homework more than two days late will not be accepted. The six highest homework scores will contribute to 30% of your final grade.

A midterm is tentatively scheduled during class time on Monday, February 15. It will be administered remotely and monitored via Zoom or Respondus LockDown Browser. Your webcam must be operational and positioned so that your hands and entire workspace are visible. I reserve the right to require an oral examination during a live video conference on Zoom in order for you to justify any work that you have submitted. If you foresee any issues with this policy based on your testing environment, please notify me as soon as possible.

inal project presentation is scheduled
for the last week of classes and happens via Zoom. The project may be targeted towards either the theoretical or the applied aspect of probability and is due on Friday, March 19. Makeup presentations will only be offered in the event of extreme circumstances. If you think you have a problem which will force you to miss the presentation, please come talk to me as soon as possible.

Help: Additional handouts will be distributed throughout the quarter. Students are also encouraged to ask for individualized help from the instructor at any time.

Students with Disabilities: If you qualify for academic accommodations because of a disability or medical issue, please submit a faculty letter to me from Disability Services Program (DSP) in a timely manner so that your needs may be addressed. DSP determines accommodations based on documented disabilities/medical issues. DSP is located on the 4th floor of Ruffatto Hall, 1999 E Evans Ave, 303-871-2278. Information is also available online at; see the Handbook for Students with Disabilities.

Honor Code: Follow the Honor Code in all activities related to this course. Incidents of academic misconduct will be reported to and investigated by the Office of Student Conduct.

Religious Accommodations: University policy grants students excused absences from class or other organized activities for observance of religious holy days, unless the accommodation would create an undue hardship. Faculty are asked to be responsive to requests when students contact them in advance to request such an excused absence. Students are responsible for completing assignments given during their absence, but should be given an opportunity to make up work missed because of religious observance. Once a student has registered for a class, the student is expected to examine the course syllabus for potential conflicts with holy days and to notify the instructor by the end of the first week of classes of any conflicts that may require an absence (including any required additional preparation/travel time). The student is also expected to remind the faculty member in advance of the missed class, and to make arrangements in advance (with the faculty member) to make up any missed work or in-class material within a reasonable amount of time.

Other: Check the DU academic calendar for important dates throughout the quarter:

C'est la vie: I fully understand that unlike in 'ordinary' quarters, you may be dealing with a lot of issues that are unusual and unrelated to your coursework. In particular, you may have a lot on your mind besides this course. If you need extra help or support, please reach out to me! I will do whatever I can to accommodate you.

Note: Homework assignments on this page are subject to change, and updates will be posted on Canvas.

Work the following homework problems at the appropriate time.

Chapter #
Theoretical Exercises
2, 6, 7, 14, 15, 18, 19, 23, 24, 28, 30
5, 6, 9
3, 8, 9, 10, 13, 18, 21, 22, 25, 38, 45
50, 54
2, 3, 7, 11, 15, 16
4, 9