**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)