226a – Random Processes in Systems 8/30/2006 Jean Walrand EECS – U.C. Berkeley
Outline Administrative Course Outline
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 Prof. Jean Office Hours: Tu-W 3:00-4:00, 257M Cory HallCory Hall GSI: Assane Gueye Office Hours: TBA
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
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
Linear Algebra A
Probability P(.) X( ) Y( ) X( ) ^ g(.) X( ) Y( )
Gaussian Random Vectors
y x f(x, y)
Detection / Hypothesis Testing Z( ) X Y( ) X( ) ^ g(.) Noise Detector
Estimation Z( ) X Y( ) X( ) ^ g(.) Noise Estimator X R
Laws of Large Numbers CLT: Examples
Markov Chain: Discrete Time Chain 1
Markov Chain: Discrete Time Chain 2
Poisson Process Poisson01 = 0.01
Poisson Process Poisson01 = 0.04
Markov Chain: Continuous Time Chain 3
Renewal Process renewal1 i.i.d. U[0, 10]