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Spring 2012

IC666: Discrete Stochastic Processes (Spring 2012)

Instructor:
Kyung-Joon Park
Office hours: By appointment, 3-309 DGIST

Textbooks:

• Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2nd edition, 2008
• Discrete Stochastic Processes, Robert G. Gallager, Springer, 1995. (Draft of the second edition, "Stochastic Processes: Theory for Applications," freely available at http://www.rle.mit.edu/rgallager/notes.htm)

Course Description:
The purpose of this course is to build a conceptual understanding of tractable classes of models on discrete stochastic processes. We study applications of probabilistic models in various areas. We also cover the essentials of the undergraudate-level probability course in order to gain a concrete understanding of basic probability models.

Grading policies:
Exam 70%, Homework 30%

Announcement:

• Assignment 1 (due: March 29) | Solutions
• Assignment 2 (due: April 12) | Solutions
• Assignment 3 (due: 2 pm, April 23) | Solutions
• Assignment 4 (due: class hour, June 14)
• Assignment 5 (due: class hour, June 14)
• The midtem exam is scheduled at 1 pm, April 24.
• The final exam is scheduled at 1:30 pm - 3:30 pm, June 15.

Lectures:

• [March 6] Introduction to probabilistic systems
• [March 8] Conditional probability, Bayes' rule, total probability theorem
• [March 13] Independence
• [March 15] Counting
• [March 20] Discrete random variable
• [March 22] No class
• [March 27] Conditional expectation
• [March 29] Multiple discrete random variables
• [April 3, 5] No class
• [April 10] Continuous random variables I
• [April 12] Continuous random variables II
• [April 17] Continuous random variables, derived distributions (regular & possible makeup class)
• [April 19] Continuous random variables, derived distributions (cont'd) (regular & possible makeup class)
• [April 24] Midterm exam
• [April 26] No class (midterm exam week)
• [May 1] Transforms
• [May 3] Iterated expectations
• [May 8] Sum of a random number of random variables
• [May 10] No class
• [May 15] Weak law of large numbers
• [May 17] Bernoulli process
• [May 22] Poisson process
• [May 24] No class (ISET 2012)
• [May 29] Poisson process: Examples
• [June 1] Poisson process: Examples (cont'd)
• [June 5] More about Poisson process
• [June 7] Problems on Poisson distribution
• [June 15] Final exam