(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
Simple-EE 