## ECE351S - Probability and Random Processes

Description: Engineers and scientists deal with systems, devices, and environments that contain unavoidable elements of randomness. To understand, analyze, and optimize in an uncertain world, probability theory is developed as a mathematical tool to logically reason about uncertainty. This course provides an introduction to probabilistic modeling, statistical techniques, and random processes for 3rd-year engineering students.

Instructor: Prof. Ben Liang
Office: BA4122 (through the doors labeled BA4113 or BA4145)
http://www.comm.utoronto.ca/~liang

Textbook: A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Second Edition, Addison Wesley, ISBN 0-201-50037-X (required).

Course Website: http://ccnet.utoronto.ca/20071/ece351h1s
Homework, handouts, grades, and announcements will be posted here.

Lectures:
Mondays 15:10 - 16:00; BA1200
Wednesdays 16:10 - 18:00; BA1220

Office Hours:
Mondays 16:10 - 17:00
Tuesdays 14:10 - 15:00
Wednesdays 15:10 - 16:00
Thursdays 13:10 - 14:00

Homework: Homework will be assigned and collected each week. This is a course almost completely in mathematics, where each new concept builds on previous concepts. To do well in this course you must keep up-to-date with the class schedule. The best way to make sure of this is to work out  the homework questions before new materials are covered.

Grading Policy:
Homework: 10%
Midterm Exam: 40%
Final Exam: 50%

Tutorials:
TUT01: Mondays 16:10 - 17:0; BA3004
TUT02: Mondays 16:10 - 17:0; BA2159

Approximate Schedule of Topics: (See course website for actual lecture-by-lecture schedule.)

• Week 1: Experiments, models, counting, set operations (Chapters 1.1-2.3)
• Week 2: Axioms of probability, conditional probability (Chapters 2.2, 2.4)
• Week 3: Bayes' Rule, independence, sequential experiments (Chapters 2.5-2.6)
• Week 4: Random variables (RV), CDF, PDF (Chapters 3.1-3.4)
• Week 5: Function of a RV, expectation, Markov and Chebyshev Inequalities (Chapters 3.5-3.7)
• Week 6: Moments, transforms, random vectors (Chapters 3.6, 3.9, 4.1)
• Week 7: Reading Week
• Week 8: Joint distribution, independence, conditional distribution and expectation (Chapters 4.2-4.5)
• Week 9: Functions of two RVs, correlation and covariance, jointly Gaussian RVs (Chapters 4.6-4.8)
• Week 10: Mean square estimation, sums of RVs, Law of Large Numbers (Chapters 4.9, 5.1-5.2)
• Week 11: Central Limit Theorem, random processes, moments (Chapters 5.3, 5.5, 6.1-6.2)
• Week 12: Discrete-time and continuous-time random processes (Chapters 6.3-6.4)
• Week 13: Stationary processes, ergodicity (Chapters 6.5, 6.7)

Last Modified: March 2007.