This course introduces the probability theory and its applications.

Prerequisites

Textbook

Abraham H. Haddad, Probabilistics Systems and Random Signals, Pearson Prentice Hall, , 2006. ISBN 0-13-009455-2

Topic

• Chapter 1 - Introduction

  • What is Probability

Chapter 2 - Basic Probability

• Set Theory and Events
• Axioms of Probability
• Conditional Probability and Independence
• Total Probability and Bayes's Rule

Chapter 3 - Basic Probability

• Set Theory and Events
• Axioms of Probability
• Conditional Probability and Independence
• Total Probability and Bayes's Rule

• Chapter 4 - Function of a Random Variable and Expectations

  • Function of a Random Variable
  • Expectations
  • Moments, Mean, and Variance

  Chapter 5 - Two Random Variables

  • Joint Distribution Function
  • Joint Probability Mass Function
  • Joint Probability Density Function
  • Indepedence
  • Gaussian Random Variables

  Chapter 5 - Expectations and Functions

  • Expectations of Two Random Variables
  • Linear Estimation

  Chapter 12 - Expectations and Functions

  • Introduction to Random Processes
  • Distributions of Random Processes
  • Mean and Autocorrelation Function
  • Cross-Correlations