ACM/EE 116

Introduction to probability and random processes with applications.

 

Last Update: November 3, 2009

 

There will be no class on Thursday October 8, 2009.

 

Homeworks:

  1. Homework 1: Handed out on October 6, 2009, due on October 20, 2009. pdf
  2. Homework 2: Handed out on Oct 20,  2009, due on November 3, 2009. pdf
  3. Homework 3: Handed out on Nov 3, 200, due on Nov 17, 2009. pdf

 

 

Lecture Notes:

  1. Week 1 (class 1 and 2)
  2. Week 2 (class 3 and 4)
  3. Week 3 (class 4 and 5)
  4. Week 4 (class 6 and 7)
  5. Week 5 (class 7 and 8)
  6. Week 6 (class 9 and 10)
  7. Week 7 (class 10 and 11)
  8. Week 8 (class 12 and 13)
  9. Week 9-10 (class 14 and 16)

 

Prerequisite: An introductory/elementary course in probability theory and some elementary linear algebra.

 

Instructor: Houman Owhadi

  1. Office hour: Thu 12:00 pm-1:00 pm, Firestone 302.

 

 

TA: 

 

Schedule

Classes are scheduled from 10:30am to 11:55am on Tuesdays and Thursdays in 306 Firestone.

 

Grading:

Active participation in class: bonus  (There will be "in class" exercises)

Homework (4 problem sets, one every 2 weeks): 100%

 

 

Syllabus:

  1. Probability spaces.

  2. Sigma algebras.

  3. Independence, Bayes formula.

  4. Continuous random variables.

  5. Expectation, variance.

  6. Generating functions and their applications.

  7. Some important random variables and their applications.

  8. Borel Cantelli.

  9. Strong Law of Large Numbers. Monte Carlo Simulations.

  10. Modes of Convergence.

  11. Central Limit Theorem.

  12. Large Deviations (basic concepts)

  13. Conditional expectation. Filtrations.

  14. Martingales (definition, limit theorems, optimal stopping times, inequalities)

  15. Concentration of Measure (basic concepts, proof of McDiarmid's inequality as a martingale inequality).  

  16. Poisson processes.

  17. Markov chains (basic concepts).

  18. Branching processes.

  19. Gaussian processes.

           

 

 

Textbooks: The lectures will not follow closely any of those textbooks, they are given here only as suggestions

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

  2. A second course in probability theory (Sheldon M. Ross and Erol A. Pekoz) (contains "almost" everything you will learn in ACM/EE 116, very well written).

  3. chapter 2 of Lawrence C. Evans lecture notes, available at http://math.berkeley.edu/~evans/SDE.course.pdf ,

  4. Introduction to probability models (Sheldon M. Ross).

  5. Probability and random processes for electrical and computer engineers (John A. Gunber)

  6. Probability and random processes for electrical engineering (Alberto Leon-Garcia).

  7. Introduction to probability (Dimitri P. Bertsekas).

  8. Introduction to probability (Charles M. Grinstead and J. Laurie Snell).