544 syllabus

George Mason University
Volgenau School of Engineering
Department of Statistics

STAT 544 Applied Probability

Fall Semester, 2021

Section 003

Wednesdays from 7:20 to 10:00 PM (starting Aug. 25, with other dates given below)

Location: room 1107 of Nguyen Engineering Building

Instructor: Clifton D. Sutton

office: Room 1706, Nguyen Engineering Building
phone: (703) 993-1684
fax: (703) 993-1700 (a shared fax machine in department office ... so use a cover sheet and let me know if you send something (but try to avoid doing so))
e-mail: csutton@gmu.edu

office hours:

6:15-7:00 (in room 1707 of the Nguyen Engineering Building) & 10:00-10:30 PM (in the class room) on class nights,
plus one virtual office hour each week (with the times given in the weekly folders of the course Blackboard site)

Text:

A First Course in Probability, 10th Ed. , by Sheldon Ross (Prentice Hall, 2014)
(Note: The official text book is the regular United States edition. The International Edition may not be the same book. (In the past some students have used the International Edition, but the page numbers differed, and the book did not even have the same number of chapters. So it may be a bit frustrating if you try to use the International Edition.))

Prerequisite:

three semesters of calculus and an undergraduate course covering calculus-based probability (like STAT 346)

Description:

This course covers elementary probability, reviewing concepts students should already have been exposed to and adding more results and methods to what is typically covered in an undergraduate probability course. After covering simple combinatorics and the axioms of probability and some of their consequences, the course covers conditional probability, independence, random variables, common discrete and continuous distributions, joint distributions, expectation, limit theorems, and assorted other topics.

Approximate week-by-week content:

[1] Aug. 25:: combinatorics
[Ch. 1 of text]
[2] Sep. 1:: axioms of probability and some results which follow from them
[Ch. 2 of text]
[3] Sep. 8:: conditional probability and independence
[Sec. 3.1 through Sec. 3.3 of text, and some of Sec. 3.4]
[4] Sep. 15:: more on independence and conditional probability; discrete random variables and their expected values
[Sections 3.4, 3.5, 4.1, 4.2, and 4.3 of text]
[5] Sep. 22:: more on discrete random variables and expectation, discrete distributions based on iid Bernoulli random variables (binomial, geometric, and negative binomial distributions), and expectations of sums of discrete random variables
[Sec. 4.4 through Sec. 4.6 of text, part of Sec. 4.8 of the text, and Sec. 4.9 of the text]
[6] Sep. 29:: other discrete distributions and more results pertaining to random variables; Poisson processes; continuous random variables
[Sec. 4.7, part of Sec. 4.8, & Sec. 4.10 of text; Sec. 9.1 of text; and Sec. 5.1 & 5.2 of text]
[7] Oct. 6:: more on continuous random variables (including functions of cont. r. v's)
[Sec. 5.2 and Sec. 5.7 of text]; 1st Midterm Exam (on Ch. 1 through Ch. 3 (closed book and notes));
[8] Oct. 13:: common continuous distributions, and random variate generation
[Sec. 5.3 through Sec. 5.6 of text, and Ch. 10 through subsection 10.2.1 of text]
[9] Oct. 20:: joint distributions and independent random variables
[Sec. 6.1 through Sec. 6.3 of text]
[10] Oct. 27:: conditional distributions, order statistics
[Sec. 6.4 through Sec. 6.6 of text]
[11] Nov. 3:: more on joint distributions, more on expectation
[Sec. 6.7 of text, and Sec. 7.1 through Sec. 7.3 of text]
[12] Nov. 10:: covariance and correlation
[Sec. 7.4 of text]
2nd Midterm Exam (on Ch. 4 & Ch. 5 (open book and notes));
[13] Nov. 17:: conditional expectation, moment generating functions
[Sec. 7.5 and Sec. 7.7 of text]
[**] Nov. 24:: no class due to Thanksgiving recess
[14] Dec. 1:: more on expectation and normal random variables, limit theorems (and inequalities)
[Sec. 7.8 & Sec. 7.9 of the text, Sec. 8.1 through Sec. 8.4 of text]
[**] Dec. 8:: Final Exam
(note: exam period is from 7:30 to 10:15 PM)

Note: If any classes are cancelled due to bad weather (or for any other reason), some of the dates given above may be changed (including the dates for the exams).

Learning Outcomes:

Master the basics of elementary probability typically covered in a one-semester undergraduate probability course.
Extend your knowledge of probability by understanding more advanced results and techniques.
Be able to solve probability problems in a sensible manner and clearly communicate your solutions using proper terminology and notation. (It's not enough to just get correct answers. You should also present easy-to-follow and clearly-written solutions, using standard notation and terminology.)

Grading:

20% for homework assignments (your best 10 of 12 assignment scores will be averaged to determine this portion of your overall average)
10% for quizzes (your best 10 of 11 quiz scores will be averaged to determine this portion of your overall average)
20% for closed book (and notes) midterm exam based on Chapters 1-3
20% for open book (and notes) midterm exam based on Chapters 4 & 5
30% for open book (and notes) final exam
(Note: If you miss a midterm exam, instead of giving you a make-up exam I'll just let your final exam score be worth 50% instead of 30%. Also, even if you take both midterm exams, if you do better on the final exam than you did on one of the midterm exams, I'll not count your lower midterm exam score and increase the weight of your final exam score to 50%.)

Additonal Comments:

Put STAT 544 in the subject line when you send me e-mail (due to spam, I sometimes delete messages without reading them, based on the subject line).
Be sure to note that there is not a class meeting scheduled for Wed., November 24 (due to Thanksgiving recess).
Please do not leave long messages on my voice-mail. Always leave your phone number, if you want me to return your call, speaking slowly, even though you might have given it to me previously. I find it better to communicate with people in person or via e-mail --- phone tag is frustrating and sometimes the GMU voice-mail system doesn't work the way it is supposed to.
All homework should be on paper which is approximately 8.5 inches by 11 inches. All pages should be stapled in the upper left hand corner. All answers should be clearly indicated. (You need to choose one answer for each part. Draw a box around your final answers or highlight them in some way.) You should show adequate supporting work and not merely give answers (in most cases).
You are expected to familiarize yourself with the George Mason University honor code and abide by it. It is perfectly okay to seek assistance from others on any of the homework problems (except for extra credit problems, which may be occassionally assigned), but you should not turn in any work that is copied from someone else (and so you should be prepared to explain your solution to me if asked to do so). To further clarify, while it's okay to briefly discuss homework problems with other students, you should not look at another student's work while writing up your homework solutions. Nor should one student provide or explain most every step of his/her solution to another student.) It will be considered to be a violation of the honor code if you deviate from this rule concerning homework or if you give or receive aid on the exams.
You are expected to take the final exam during the designated time slot; Incompletes will not be granted except under very unusual circumstances.
Please abide by the university policy that cell phone ringers be turned off while class is in session.
Please do not make a lot of noise eating during class --- if you feel that you must eat during class, please choose a soft candy bar rather than a bag of potato chips (since both the chips and the bag they come in tend to make too much noise when eaten and handled).
If you are a student with a disability and desire academic accommodations, please see me during the first two weeks of classes and contact the Office of Disability Services (ODS). All academic accommodations must be arranged through the ODS.
Any class meetings canceled by the university due to snow, sleet, power outage, bombing, etc. will be made up. If the university doesn't announce a make-up date, the lecture will be presented on the course Blackboard site.
With regard to bad weather, I will plan to teach class if the university is open and not teach it if the university is closed. So instead of calling or e-mailing me to find out if I plan to have class, just find out if the university is open or closed.
Caveat: The schedule and procedures described here for this course are subject to change (and it is the responsibility of students to attend all class meetings and keep themselves informed of any changes).