ACM/EE 116
Applied Probability and Applications

Announcements

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

TA #1
Roger Donaldson
Office: Firestone 216
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: Firestone
Phone:
Office Hours:
Email: mulinch@caltech.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: 30%
Exams: 60% (There will be two take-home exams.)

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.
5. 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)

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
HW #2
HW #3
HW #4

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

Midterm
Final

Midterm Grades
Grades for your midterm reports have been assigned according to your raw midterm exam scores as follows. The maximum possible midterm exam score is 60. Homework and class participation grades are not accounted for in your midterm reports, but will be included in your final grade.

A+	55-60
A	45-54
A-	40-44
B+	37-39
B	35-36
B-	33-34
C+	30-32
C	27-29
C-	24-26
D	0-23