ECE302 Course Outline, Spring 2013, Prof. Boutin

Part 1: Foundations (To be tested in the first intra-semestrial exam)

Week 1-3 (Lecture 1, 2, 3, 4, 5, 6, 7, 8, 9)

• 1.1 Sets
  • Definition
  • Operations
  • De Morgan's Law
• 1.2 Probability Models
  • Sample spaces
  • Probability Laws (axioms, properties
• 1.3 Conditional Probabilities
• 1.4 Independence
• 1.5 Bernoulli Trials
• 1.6 Counting

Suggested references:

Chapter 1 and 2 of the textbook,

Chapter 1 of "Introduction to Probability," by Dimitri P. Bertsekas and John N. Tsitsiklis. Athena Scientific, Belmont, Massachusetts, 2008, ISBN 978-1-886529-23-6.

Foundations of Probability Theory: Basic Definitions, module by Don Johnson posted on Connexions

Part 2: Discrete Random Variables (To be tested in the second intra-semestrial exam)

Week 4-5(6) (Lecture 10,11, 12, 13, 14, 15, 16, (17) )

• 2.1 Definition and examples
• 2.2 Functions of a discrete random variable
• 2.3 Moments of discrete random variable (expectation, variance)
• 2.4 Conditioning of a discrete random variable
• 2.5 Independence of discrete random variables

Suggested References

Chapter 3 in the textbook

Chapter 2 in "Introduction to Probability," by Dimitri P. Bertsekas and John N. Tsitsiklis. Athena Scientific, Belmont, Massachusetts, 2008, ISBN 978-1-886529-23-6.

Chapter 4 of Collaborative Statistics by Illowski and Dean (available online)

Part 3: Continuous Random Variables (To be tested in the second intra-semestrial exam)

Week (6)7- ? (Lecture (17) 18,19,20,... )

• 3.1 Definition of continuous random variable, probability density function.
• 3.2 Moments of a continuous random variables (expectation, variance)
• 3.3 The cumulative distribution function of a random variable (discrete or continuous)
• 3.4 Normally distributed random variables.
• 3.5 Focus on 2D random variables: expectation, conditioning, and independence.
• 3.6 Function of a random variable
• 3.7 Moment Generating (Characteristic) Function (for 1D discrete/continuous random variables)
• 3.8 Pairs of jointly Gaussian Variables

Suggested References

Chapter 4,5,6 in the textbook

This tutorial on the bivariate normal (from a supplement to "Introduction to Probability," by Dimitri P. Bertsekas and John N. Tsitsiklis. Athena Scientific, Belmont, Massachusetts, 2008, ISBN 978-1-886529-23-6).

Part 4: Random Processes (To be tested in the final exam)

Week 11-15

• 4.1 Introduction, Definition of Random Processes (CT and DT)
• 4.2 Characteristics of Random Processes
• 4.3 Examples of DT Random Processes; Sum Processes
• 4.4 The Poisson Random Process and its relationship to Binomial Counting
• 4.5 LTI systems and Random Processes

Chapter 9,10 in the textbook.

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