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California Institute of Technology
Department of Computing + Mathematical Sciences
ACM/EE 116 Introduction to Probability Models
Fall 2016
Lectures:
Instructor:
Office:
Email:
Website:
Office Hour:
Teaching Assistants:
TTh 9:00-10:20 in 105 ANB
Konstantin (Kostia) Zuev
114 ANB
[email protected] (please include “116” in the subject line)
http://www.its.caltech.edu/~zuev/
Th 15:00-16:00, or by appointment (please, send an email to schedule)
Nikola Kovachki ([email protected], Mon 15:00-16:00, 243 ANB)
Albert Chern ([email protected], Tue 15:00-16:00, 314 ANB)
Yu Su ([email protected], Wed 12:00-13:00, 231 ANB)
Brennan Young ([email protected], Wed 15:00-16:00, 106 ANB)
Navid Azizan ([email protected], Thu 16:00-17:00, 238 ANB)
Leiya Ma ([email protected], Fri 15:00-16:00, 105 ANB)
Course Description
This course introduces students to the fundamental concepts, methods, and models of applied probability and stochastic
processes. The course is application-oriented and focuses on the development of probabilistic thinking and intuitive feel
of the subject rather than on a more traditional formal approach based on measure theory. The main goal is to equip
science and engineering students with necessary probabilistic tools they can use in future studies and research.
Prerequisites
• Ma 2, Ma 3 or instructor’s permission.
• Some familiarity with MATLAB, e.g. ACM 11, is desired.
Textbooks
• S.M. Ross, Introduction to Probability Models, Academic Press 2009.
• J.A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge, 2006.
• Instructor’s Notes (will appear at the course website after each lecture)
Course Plan
The following is a detailed tentative outline of the topics to be covered this term.
• Probability models, basics of probabilities: sample spaces, axioms, independence
• Random variables: discrete and continuous, expectation, moments, variance, covariance
• Independent random variables, moment generating functions, Poisson paradigm
• Markov’s and Chebyshev’s inequalities, law of large numbers, central limit theorem, Monte Carlo method
• Conditional probability, conditional expectation, conditional variance
• Law of total expectation, application to the quick-sort algorithm analysis
• Compound random variables, computing probabilities by conditioning
• Classification of Poisson events, the best prize problem, the ballot problem, double conditioning
• Application: probabilistic analysis of random graphs
• Random vectors, covariance matrix, Karhunen–Loève expansion, transformation of random vectors
• Wiener filters, Gaussian vectors, joint probability density function
• Stochastic processes, Markov chains, counting processes, Poisson processes
• Interarrival and waiting times, generating the Poisson process
• Merging and splitting Poisson processes, conditional distribution of the arrival times, order statistics
• Multi-type Poisson process, application to insurance, health care, and traffic engineering
• Brownian motion (Wiener process), hitting times, and maximum variable
• General stochastic processes, the mean and correlation functions, stationary processes
• Gaussian processes, estimation of the correlation function, power spectral density
Grading
Your final grade will be based on your total score. Your total score is a weighted average of Homework (50%), Midterm
exam (20%), Final exam (20%), and Quizzes (10%). You can increase your total score by up to 5% (not exceeding 100%
in total) if you participate actively in Piazza discussions in the Q&A section. Every answer submitted before TAs or
instructor answer, which is later endorsed as “good answer” by TAs or instructor, gets 1% of the total score. The limit is
5 answers per student. There are no fixed thresholds for grades, but if your total score is 90% (80%, 70%, 60%), you are
guaranteed at least “A” (“B”, “C”, “D”).
Homework
There will be six homework assignments. Homework problems and due dates will be posted on the course website (for
exact dates see “Important Dates” below). Solutions will be posted on Piazza (see below). Late homework will not be
accepted for any reason, but the homework with the lowest score will be dropped and not counted toward your total
score. Extensions may be granted for academic (with at least one week’s notice) or medical reasons.
Exams
There will be two in-class exams: midterm and final. The exams are closed-book, but you can use your own notes. You
can (but need not to) use a calculator, but no other electronic devices are permitted (no computers, phones, etc).
Quizzes
There will be two ~10 min quizzes given on two random days. Each quiz will consists of five true/false questions. For
each quiz you will get 5 points for participation, plus 1 point for each correctly answered question.
Collaboration Policy
If you get stuck with a homework problem, I encourage you to discuss it with other students. But you will have to
prepare and submit your homework by yourself. No collaboration is allowed on the midterm and final exams.
Important Dates
Quizzes:
Homework:
Midterm:
Final:
random, mark your calendar
Oct 4 (due 11), Oct 11 (18), Oct 18 (25), Nov 3 (10), Nov 10 (17), Nov 17 (29)
Thursday, October 27
Thursday, December 8
Websites
Lecture notes, homework assuagements, due dates, and other course related information and materials will be posted on
the course website. You are expected to check it regularly.
http://www.its.caltech.edu/~zuev/teaching/2016Fall/ACM116.html
Class discussion will be managed via Piazza, which is designed such that you can get a quick help from your classmates,
the TA(s), and the instructor. Instead of emailing questions to the teaching staff, I encourage you to post your questions
on Piazza because a) you will get the answers faster b) your classmates may also benefit from seeing the answers to your
questions. Enroll here:
https://piazza.com/caltech/fall2016/acm116
Honor Code
You must conform to the honor code:
“No member of the Caltech community shall take unfair advantage of any other member of the Caltech community.”
In-Class Behavior
Behavior that persistently or grossly interferes with classroom activities is considered disruptive behavior and may be
subject to disciplinary action. Such behavior inhibits other students’ ability to learn and an instructor’s ability to teach. A
student responsible for disruptive behavior may be required to leave class pending discussion and resolution of the
problem and may be reported to the Undergraduate Board of Control or the Graduate Honor Council. In particular, the
use of cell phones during class or conversation is disruptive behavior.
Academic Integrity
All students are responsible for maintaining standards of academic integrity. In particular, collaboration during midterms
or the final are strictly prohibited.
This syllabus is not a contract, and the Instructor reserves the right to make some changes during the term.