June 2014
Northwestern University Program in Public Health (PPH)
Course Syllabus
Epi-Bio 303: Introduction to Probability Theory
Fall Quarter 2014 (Sept. 24- Dec. 8)
Time: Monday and Wednesday 10:30-12:00
Location: Lurie – Gray Seminar Room
Course Instructor:
Mary Kwasny, ScD
Associate Professor
m-kwasny@northwestern.edu
(312) 503-2294
Office hours: Friday 10:00-11:00
I. Course description
This is an introductory course to the theory of probability. It will focus on reviewing the fundamentals of
calculus, introducing probability distributions and their properties, reviewing and applying matrix algebra
notation to functions of random variables, and introducing point estimation and the central limit theorem
in a theoretical framework. Specifically, the course will focus on probability concepts, distributions
(expected value, variance, and moment generating functions), law of large numbers, and the central limit
theorem.
II. Learning Objectives
This course concentrates on establishing a solid foundation of probability theory and review of calculus
and matrix notation so that the theories presented in Statistical Inference can be more readily
understood and the students may be able to apply these principles as practicing statistical analysts.
Upon completion of the course, students will be able to:
 Apply basic probability concepts such as conditional probabilities, independence, Bayes’ Rule,
and combinations and permutations to calculate probabilities of events of practical interest.
 Describe and apply concepts of discrete and continuous random variables, density functions,
joint, marginal, and conditional distributions, and sampling distributions of statistics such as the
mean.
III. Texts and reading
Hogg and Tanis. Probability and Statistical Inference, 8th edition. Prentice Hall. Upper Saddle River, NJ.
2010. ISBN-10: 0-321-58475-9. ISBN-13: 978-0-321-58475-5.
Grinstead and Snell. Introduction to Probability. (Available from the AMS Bookshop under the GNU Free
Documentation License (FDL).
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf
Handouts posted on the course website.
Blackboard™
The syllabus and selected readings will be posted on the course’s Blackboard site, available at
https://courses.northwestern.edu/webapps/login if you are registered for the course.
June 2014
IV. Class assignments, projects, quizzes, tests
There will be six assignments (homeworks) which will be due in class on Wednesdays, unless otherwise
specified. You are expected to work on these independently, but may ask questions pertaining to them
in class or during office hours. This is to provide you with the opportunity to diagnose where you may not
fully understand the material. There will be a midterm and final exam.
V. Student Evaluation
Since much time is dedicated on the homework, these will be worth 35% of your grade. We will have
some in-class group worksheets that will be worth 10%. The mid-term will be worth 25% and the final
will be worth 30%. By nature of the course, the final will be cumulative, but will emphasize material from
the latter half.
Course evaluation
The PPH Program administers web-based course evaluations to students for each course near the end
of the quarter. Your completion of both the unit (course) and faculty evaluation components is
required; failure to complete either of the evaluations will result in an incomplete grade until the
evaluations are submitted. You will be sent the web link and instructions via email later in the quarter.
You will have about two weeks to complete the evaluations before grades are submitted.
Academic Integrity
Every Northwestern faculty member and student belongs to a community of scholars where academic
integrity is a fundamental commitment. The Program in Public Health abides by the standards of
academic conduct, procedures, and sanctions as set forth by The Graduate School at Northwestern
University. Students and faculty are responsible for knowledge of the information provided by The
Graduate School on their Web page at http://www.tgs.northwestern.edu/academics/academicservices/integrity/index.html
Academic misconduct includes, but is not limited to
1. Receiving or giving unauthorized aid on examinations or homework
2. Plagiarism
3. Fabrication
4. Falsification or manipulation of academic records
5. Aiding or abetting any of the above
The PPH follows The Graduate School’s procedure for evaluating alleged academic misconduct, as
outlined on the TGS website. http://www.tgs.northwestern.edu/academics/academicservices/integrity/dishonesty/index.html
Faculty reserve the right to use the “Safe Assignment: Plagiarism Detection Tool” that is part of the
Course Management System to evaluate student assignments. Information about this tool can be found
at http://www.it.northwestern.edu/education/coursemanagement/support/assessments/safeassignment.html
June 2014
Class schedule
Week
Date
0.5
9/24
1.5
9/29,
10/1
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10/6,
10/8
10/13,
10/15
10/20,
10/22
10/27,
10/29
11/3,
11/5
11/10,
11/12
11/17,
11/19
11/24,
11/26
Topic
Course intro & Pre-test
Calculus review
Basic probability concepts:
Distributions, Densities
Permutations and
combinations
Reading
Handout on
course website
Assignments
G&S Ch 1& 2
G&S Ch 3
Discrete Distributions
H&T Ch 2
Continuous Distributions
H&T Ch 3
Hmwk 1
Hmwk 2
Hmwk 3
Review and Midterm(Wed)
Matrix Algebra review
Jointly distributed random
variables
Distributions of functions of
random variables
Law of large numbers
(central limit theorem)
- Thanksgiving
Central Limit theorem, Cont
Review
FINAL EXAM
Handout on
course website
H&T Ch 4
H&T Ch 5
Hmwk 4
Hmwk 5
Hmwk 6
G&S Ch 8 & 9
12/1
12/3
11.
12/8
Optional/recommended reading
10.
Keisler, H.J. Elementary Calculus: An Infinitesimal Approach. On line edition, 2000, revised 2012.
http://www.math.wisc.edu/~keisler/calc.html
Ross, Sheldon. A First Course in Probability. (any Edition). Previously published by Macmillan, now by
Pearson Prentice Hall.
Dekking, Kraaikamp, Lopuhaa, and Meester. A Modern Introduction to Probability and Statistics:
Understanding How and Why. Springer-Verlag 2005. London.