1

Decision Sciences Department

COURSE
NUMBER: DNSC 6206 (Fall 2020)

COURSE
TITLE: Stochastic Foundations: Probability Models

COURSE
DESCRIPTION: This course introduces the foundations of Probability, along with the
commonly used Probability models (Binomial, Normal, and Poisson) in
predictive analytics. Topics covered include probability laws, probability
models for modeling dependence, univariate and bivariate models and their
applications, conditional mean models including simple regression and
extensions to probit and logit models and classification models.

COURSE
PRE-REQS: MSBA Program Candidacy or instructor approval.

PROFESSORS: Refik Soyer, Professor of Decision Sciences and of Statistics
Office: Funger Hall, 415 B
Phone: 202-994-6445
E-mail: [email protected]
Office Hours: TBA

TEXTBOOKS: Probability and Statistics, 4th Edition
M. H. DeGroot and M. J. Schervish (Strongly Recommended)
Addison-Wesley, 2012, ISBN: 978-0-321-50046-5

COURSE
OBJECTIVES: To provide students with an understanding of
• Key probability concepts and graphical representations
• The basic probability models and related probability distributions
(normal, binomial, and Poisson)
• Commonly used measures for univariate and bivariate distributions
(means, variances, co-variances)
• Conditional mean models, regression and classification models and
their applications.

SOFTWARE: The course will primarily involve using R.

2

COURSE SCHEDULE

Session Date Subject/Topic Readings
1
Dealing with uncertainty.
Interpretations of probability. Concept of
a random experiment. Special random
quantities: Events and random variables.
Bernoulli trials and categorical random
variables. Introduction to rules of
probability. Defining conditional
probability.
DeGroot & Schervish
(DS) Ch. 1.1-1.10, Ch.
2.1
2
Concept of dependence.
Conditional probability and dependence.
Categorical random variables and
contingency table models. Law of total
probability and Bayes’ rule. Graphical
representations for probability models:
trees for probability computations and
graphical models for describing
dependence.
DS Ch. 2.1-2.3

3-4
Random variables (RVs): Discrete
RVs and univariate and multivariate
probability distributions.
Probability mass and density functions.
Cumulative distributions. Means and
variances for random variables.
Covariance of random variables.
Conditional means and variances.
DS Ch. 3.1-3.6
(Discrete RVs part)
Ch. 4.1-4.7
(Discrete RVs part)

4-5
Commonly used univariate
probability models (Discrete RVs).
Binomial, Geometric, Poisson, and
Multinomial. Applications.
DS Ch. 5.1-5.5 and
Ch. 5.9

5-6
Introduction to continuous RVs:
Uniform, exponential, gamma, normal
and bivariate normal probability models.
Applications.
DS Ch. 3.2-3.3
Ch. 4.1-4.3, 4.6- 4.7
Ch. 5.6-5.7, 5.10

7
Regression and classification models.
Conditional mean and introduction to
normal regression model. Logit, probit
and other classification models.
Applications.
DS Ch. 4.7, DS Ch.
DS Ch. 11.1-11.2 (up
to page 702).

8 Final Exam October 21, 2020

3

ASSIGNMENT OF CREDIT HOUR POLICY: Students will spend about 2 hours per week in
online sessions. Required readings, videos and assignments for the course are expected to average 8
hours per week. All online sessions during the regular class time (W 4:30 -7:00 pm) will be recorded.
There will be additional on-line sessions scheduled for students who will participate from abroad.

Students are expected to attend the online sessions 1) having read the material for the current
lecture; 2) having watched pre-session recordings; 3) having reviewed the material of the previous
lectures.

WEEKLY PROBLEM/REVIEW SESSIONS: There will be problem/review sessions on
Fridays 4:00-5:30 pm starting on September 11th. These sessions will be recorded and recordings will
be posted as soon as they become available. Attendance to the problem/review sessions are
voluntary. The sessions will be taught by doctoral students. An additional review session will be
scheduled for students who will participate from abroad.

GRADING: The course grade will be based on group homework assignments, quizzes, and a final
examination according to the following weights:
Quizzes: 30%.
Homework assignments (Group effort): 30%.
Final exam: 40%.

Quizzes
There will be three on-line quizzes. They will be based on current and prior assigned readings and
material covered in the class sessions.

Homework Assignments
Homework assignments will typically require the use of software. A typical homework assignment
will consist of a few problems with several parts. Solutions will be posted on the course web site.
These are group efforts. The groups will consist of 2 OR 3 students and will be determined by the
second session. Assignments will be available by Thursday night every week and they will due on the
Saturday of the following week by 12:00 noon. For example, the assignment 1 will be posted on
Thursday September 3rd and it will be due on Saturday September 12th by 12:00 noon.
No late homework assignments will be accepted.

Submission guidelines for homework assignments
In preparing the submissions, please follow these guidelines:
Make sure the solutions are typed or easily readable by anyone;
Ensure a clear logical flow and mark your answers;
Include names of your group members on the first page.

Final Exam
The final exam is individual and is scheduled for Wednesday October 21st.

4

EXAM, QUIZZES
AND HOMEWORK
ASSIGNMENTS
SCHEDULE: The assignment schedule is tentative and might be adjusted.

Name Due Date (tentative)
Quiz 1 Session 3
Quiz 2 Session 5
Quiz 3 Session 7

HW 1 Saturday, September 12
HW 2 Saturday, September 19
HW 3 Saturday, September 26
HW 4 Saturday, October 3
HW 5 Saturday, October 10
HW 6 Saturday, October 17
Final Exam Week 8: Wednesday, October 21st.

ACADEMIC
INTEGRITY: Cheating and plagiarism will not be tolerated. Any case will automatically
result in loss of all the points for the assignment, and may be a reason for a
failing grade and/or grounds for dismissal. In case of a group assignment, all
group members will receive a zero grade. Any suspected case of cheating or
plagiarism or behavior in violation of the rules of this course will be reported
to the Office of Academic Integrity. Students are expected to know and
understand all college policies, especially the code of academic integrity
available at: http://www.gwu.edu/~ntegrity/code.html

DISABILITY
SERVICES: Any student who may need an accommodation based on the impact of a
disability should contact the Office of Disability Support Services (DSS) to
inquire about the documentation necessary to establish eligibility, and to
coordinate a plan of reasonable and appropriate accommodations. DSS is
located in Rome Hall, Suite 102. For additional information, please call DSS
at 202-994-8250, or consult www.disabilitysupport.gwu.edu.

5

ATTENDANCE: The George Washington University Bulletin, Graduate Programs, 2009–2010:
"Regular attendance is expected. Students may be dropped from any class for
undue absence…. Students are held responsible for all of the work of the
courses in which they are registered, and all absences must be excused by the
instructor before provision is made to make up the work missed."

CHANGES: The instructors reserves the right to make revisions to any item on this
syllabus, including, but not limited to any class policy, course outline and
schedule, grading policy, tests, etc. Note that the requirements for
deliverables may be clarified and expanded in class, via email, or on
Blackboard. Students are expected to complete the deliverables incorporating
such additions and to check email and Blackboard announcements frequently.

Email:51zuoyejun

@gmail.com