ELEC 4030E-4Z01/COMM 6008E-6001 Random Process 隨機程序 2010 Fall Instructor: Hsiao-Ping Tsai Office: EE711 Phone: ext.711

General Course Information Course Objective The goal of the course is to introduce the subject of probability theory and stochastic processes in engineering Classroom: EE208 Class Times: Tue. 2:10pm - 5:00pm Web site: 電機系首頁 -> 課程規章 -> 課程詳述 -> 隨機程序 隨機程序

General Course Information (con ’ t) Instructor: 蔡曉萍 (Hsiao-Ping Tsai )  Office: EE711  Phone: (04) ext. 711   Office hours: Mon.14 ： 00 ~ 16 ： 00, Wed. 10 ： 00 ~ 12 ： 00 Teaching Assistant: 尤淑佩, 尤淑佩  Office: EE 910  Phone: (04) ext. 910 

General Course Information (con ’ t) Textbook  Sheldon M. Ross, Stochastic Processes 2nd ed.  Wiley, 1996  ISBN ：  國內代理： 歐亞書局 Reference book  Roy D. Yates and David J. Goodman, Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers 2nd ed.  A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes 4th ed.

Topics Covered Basic concepts of probability and random variables (4 weeks) Poisson process (2 weeks) Renewal theory (2 weeks) Markov chains (4 weeks) Martingales (2 weeks) Random walks (2 weeks) Others: Brownian motion and Other Markov Processes (optional)

Topics Covered ( con ’ t) Basic concepts of probability and random variables  Random Variable  Probability and Expectations  Probability Inequalities Poisson Processes  Introduction  Properties  Non-homogeneous Poisson Processes  Compound Poisson Processes  Poisson Arrival See Time Average (PASTA)

Topics Covered ( con ’ t) Renewal Processes  Introduction  Limit Theorems  Key Renewal Theorems  Renewal Reward Processes  Delayed Renewal Processes  Regenerative Processes Discrete-Time Markov Chains  Introduction  Classification of States  Markov Reward Processes  Time- Reversible Markov Chains  Semi-Markov Chains

Topics Covered ( con ’ t) Martingales  Introduction  Martingals  Stopping Times  Martingale convergence Theorem  Azuma’s Inequality Random walks  Introduction  Duality in Random Walks  Remarks Concerning Exchangeable Random Walks  G/G/1 Queues and Ruin Problems  Blackwell’s Theorem

Grading Exam I: 20% (10/12) Exam II: 20% (11/16) Exam III: 20% (12/21) Final Exam: 20% (1/18) Homework: 20%

Policies Late Policy: A homework must be turned in by the midnight of its due day  5% of points will be deducted for each working day if a homework is turned in late.  A homework assignment will be counted as a Zero score once its solutions are announced. Attendance Policy: Students are obligated to present in the class. If you cannot present in the class, please ask for leave in advance.  If a student is absent from class more than 3 times, he/she might lose the chance of the grade adjustment at the end of the semester. Honesty Policy: Students are allowed to discuss problems with their classmates (or me), but they must not blatantly copy others' solutions.  A copying homework is graded zero point. Assignment Submission: Students should submit their assignments through the ecampus system or to TA.