# 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
###### 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
• The Characteristic Function
###### Week 6 Day 1
• Random Processes
• Properties of the Auto Correlation
• Power Spectral Density
• Properties of PSD