1. 226a – Random Processes in Systems 8/30/2006 Jean Walrand EECS – U.C. Berkeley

2. Outline Administrative Course Outline

3. Administrative Prereq.: EE120, EE126, and Math 54 (linear algebra), or equivalent. Lectures: Tuesdays and Thursdays 11am-12:30pm 285 Cory Discussions: Session 1 Mondays 10-11am 293 Cory Session 2 Mondays 2-3pm 299 Cory First discussion on September 12 Instructor : Prof. Jean Walrand (wlr@eecs.berkeley.edu) Prof. Jean Walrandwlr@eecs.berkeley.edu Office Hours: Tu-W 3:00-4:00, 257M Cory HallCory Hall GSI: Assane Gueye (agueye@eecs.berkeley.edu)agueye@eecs.berkeley.edu Office Hours: TBA

4. Administrative Books:  Random Processes in Systems – Lecture Notes, J. Walrand with A. Dimakis (2006) – On Line  Essentials of Stochastic Processes, Rick Durrett, 1st ed., Springer (1999).  Stochastic Processes - A Conceptual Approach, R. G. Gallager (2001) [Available from Copy Central on Hearst on 8/30] Grading:  Midterm 1 (15%)  Midterm 2 (15%)  Homework (40%)  Final exam (30%) Course Web Site:  Description – Check Announcements regularly Description  Syllabus – Check regularly: Assignments, reading, slides, notes, etc

5. Course Outline Syllabus Topics:  Preliminaries: Linear Algebra, Probability  Gaussian Random Vectors  Detection/Hypothesis Testing  Estimation  Laws of Large Numbers  Markov Chains (DT)  Poisson Process  Markov Chains (CT)  Renewal Processes

6. Linear Algebra A

7. Probability   P(.) X(  ) Y(  ) X(  ) ^ g(.) X(  ) Y(  )

8. Gaussian Random Vectors

10. y x f(x, y)

11. Detection / Hypothesis Testing Z(  ) X Y(  ) X(  ) ^ g(.) Noise Detector

12. Estimation Z(  ) X Y(  ) X(  ) ^ g(.) Noise Estimator X R

13. Laws of Large Numbers CLT: Examples

14. Markov Chain: Discrete Time 0.5 0.6 0.3 0.4 0.1 0.3 0.4 0.1 Chain 1

15. Markov Chain: Discrete Time 0.5 0.9 0.7 0.3 0.1 0.5 Chain 2

16. Poisson Process Poisson01 = 0.01

17. Poisson Process Poisson01 = 0.04

18. Markov Chain: Continuous Time 0.03 0.01 0.05 Chain 3

19. Renewal Process renewal1 i.i.d. U[0, 10]