# Course curriculum

• 1

### Introduction to Course

• Introduction to Instructor and AISciences
• Focus of the Course
• 2

### Probability vs Statistics

• Probability vs Statistics
• 3

### Sets

• Definition of Set
• Cardinality of a Set
• Subsets PowerSet UniversalSet
• Python Practice Subsets
• PowerSets Solution
• Operations
• Python Practice Operations
• VennDiagrams Operations
• Homework
• 4

### Experiment

• Random Experiment
• Outcome and Sample Space
• Event
• Recap and Homework
• 5

### Probability Model

• Probability Model
• Probability Axioms
• Probability Axioms Derivations
• Probablility Models Example
• Probablility Models More Examples
• Probablility Models Continous
• Conditional Probability
• Conditional Probability Example
• Conditional Probability Formula
• Conditional Probability in Machine Learning
• Conditional Probability Total Probability Theorem
• Probablility Models Independence
• Probablility Models Conditional Independence
• Probablility Models BayesRule
• Probablility Models towards Random Variables
• HomeWork
• 6

### Random Variables

• Introduction
• Random Variables Examples
• Bernulli Random Variables
• Bernulli Trail Python Practice
• Geometric Random Variable
• Geometric Random Variable Normalization Proof Optional
• Geometric Random Variable Python Practice
• Binomial Random Variables
• Binomial Python Practice
• Random Variables in Real DataSets
• Homework
• 7

### Continous Random Variables

• Zero Probability to Individual Values
• Probability Density Functions
• Uniform Distribution
• Uniform Distribution Python
• Exponential
• Exponential Python
• Gaussian Random Variables
• Gaussian Python
• Transformation of Random Variables
• Homework
• 8

### Expectations

• Definition
• Sample Mean
• Law of Large Numbers
• Law of Large Numbers Famous Distributions
• Law of Large Numbers Famous Distributions Python
• Variance
• Homework
• 9

### Project Bayes Classifier

• Project Bayes Classifier From Scratch
• 10

### Multiple Random Variables

• Joint Distributions
• Multivariate Gaussian
• Conditioning Independence
• Classification
• Naive Bayes Classification
• Regression
• Curse of Dimensionality
• Homework
• 11

### Optional Estimation

• Parametric Distributions
• MLE
• LogLiklihood
• MAP
• Logistic Regression
• Ridge Regression
• DNN
• 12

### Mathematical Derivations for Math Lovers (Optional)

• Permutations
• Combinations
• Binomial Random Variable
• Logistic Regression Formulation
• Logistic Regression Derivation