ACM/EE 116
Applied Probability and Applications

Announcements

• 16 December 2007.
  • Solutions to the final exam have been posted below. Have a good holiday!

Instructor
Houman Owhadi
Office Hours: Tue 2:30pm - 3:30pm

TA #1
Roger Donaldson
Office Hours: Mon 1:30pm - 2:30pm at the Red Door Cafe
Email: rdonald_at_acm_dot_caltech_dot_edu

TA #2
Mulin Cheng
Office Hours: Fri 4pm - 5pm in SFL study room 229
Email: mulinch_at_caltech_dot_edu

Prerequisites
An introductory course in probability theory and some basic linear algebra.

Schedule
Classes are scheduled from 1pm - 2:30pm on Tuesdays and Thursdays. Firestone 306.

Grading
Active participation in class: 10% (There will be "in class" exercises.)
Homework: 50%
Final Exam: 40% (This will be a take-home exam.)

Syllabus

1. Crash course in basic probability theory. (Text: Chapter 2 of Lawrence C. Evans' lecture notes, available online: http://math.berkeley.edu/~evans/SDE.course.pdf). Basic Definitions. expected value, variance, distribution functions. Independence, Borel-Cantelli lemma. Characteristic Functions.
2. Convergence theorems.
3. Strong law of large numbers. Central Limit theorem.
4. Conditional Expectation.
Poisson processes.
6. Branching Processes
7. Gaussian Vectors. Gaussian spaces.
8. Gaussian Processes.
   • Brownian Motion.
   • Ito's formula.
   • Stochastic Differential Equations.

Primary Text
Probability and Random processes (G. R. Grimmett and D. R. Stirzaker)

Other Suggested Texts
The lectures will not closely follow these texts: they are given only as suggestions.

1. Chapter 2 of Lawrence C. Evans' lecture notes, available online: http://math.berkeley.edu/~evans/SDE.course.pdf
2. Probability and random processes for electrical and computer engineers (John A. Gunber)
3. Reference for large deviations: Large Deviations for Performance Analysis by Adam Shwartz and Alan Weis http://www.math.umass.edu/~rsellis/pdf-files/Dresden-lectures.pdf

Homework
Homework will be posted here. Hand in homework at the class on the specified due date. Points will be deducted from late homeworks unless prior arrangements have been made with the TAs.

Consult any materials you like and feel free to work with other students, but be sure to you understand and write up everything you turn in.

HW #1	Available - 9 Oct 2007	Due - 16 Oct 2007
HW #2	Available - 23 Oct 2007	Due - 30 Oct 2007
HW #3	Available - 6 Nov 2007	Due - 13 Nov 2007
HW #4	Available - 27 Nov 2007	Due - 4 Dec 2007

Exams
Exams will be posted here. Exam policies are stated on the exams themselves.

Final

Available - 10 Dec 2007

Due - 14 Dec 2007, 1pm