ECE450: Probabilistic Systems in EE

(The notes below were donated by my colleague Alex Geronilla –¬†LinkedIn Here)

Chapter 1

Introduction
  • Introduction
    • Mutually exclusive
    • Marginal Probability
    • Conditional Probability
    • Baye’s Theorem
    • Equality Union sets
    • Intersection Product
    • Complement
    • Difference
  • Axiomatic Approach
Week 2 Day 1
  • Axiomatic Approach
    • Union
  • Conditional Probability
    • Total Probability
  • Independency

Chapter 2

Week 2 Day 2
  • Independent Events
  • Independent Experiments
    • Product/ Cartesian Space
  • Bernoullis Trials/ Binomial Experiments
    • De Moiure-Lapalce Theorem
  • Probability Distribution Function (PDF)
    • Properties of PDF
  • Probability Density Function (pdf)
Week 3 Day 1
  • Review of PDF and pdf
  • Mean, Values, and Moments
    • Mean Value
    • Nth General Moment
    • Central Moments
The Gaussian Random Variable
Week 4 Day 1
  • Gaussian Density Formula
  • Impulse Function
  • Phi Function
  • Densities Related to Gaussian
    • Density of Power
    • Average Power
    • Variance of the Power
    • Probability Distribution
  • Distribution
    • Average
    • Variance
  • Exponential Distribution
    • Probability Distribution
    • Average Variance
  • Uniform Distribution
    • Average

Chapter 3

Week 4 Day 2
  • Delta Distribution
  • Conditional Probability PDF/pdf
    • Arguments
    • Conditional Mean
  • Joint PDF
  • Joint pdf
    • Correlation Function
  • Conditional Probability with 2 Random Variables
  • Correlation between Random Variables
    • Covariance
    • Correlation Coefficient
Week 5 Day 1
  • Correlation Coefficient
    • Standardized Variables
    • Gaussian
  • Adding/Subtracting Random Variables
  • The Characteristic Function
Week 6 Day 1
  • Random Processes
  • Properties of the Auto Correlation
  • Power Spectral Density
    • Properties of PSD

Cheatsheets:

Quiz
Final Exam