Intro to Probability
A comprehensive introduction to probability theory, covering fundamental concepts, distributions, and applications for data-driven decision-making.
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Foundations of Probability
Unit 1: Basic Concepts of Probability
What is Probability?
Sample Spaces & Outcomes
Defining Events
Calculating Probabilities
Probability Misconceptions
Unit 2: Event Relationships and Axioms
Mutually Exclusive Events
Independent Events
Dependent Events
Conditional Probability
Axioms of Probability
Counting Techniques and Basic Probability Rules
Unit 1: Fundamental Counting Principle
Intro to Counting
FCP: Single Events
FCP: Multiple Events
FCP with Restrictions
Real-World FCP
Unit 2: Permutations
Intro to Permutations
Permutations Formula
Permutations Examples
Permutations with Repetition
Circular Permutations
Unit 3: Combinations
Intro to Combinations
Combinations Formula
Combination Examples
Permutation or Combination
Combinations in Probability
Unit 4: Basic Probability Rules
What is Probability?
Complement Rule
Addition Rule
Multiplication Rule
Rule Applications
Conditional Probability and Bayes' Theorem
Unit 1: Understanding Conditional Probability
What is Conditional Prob?
Calculating Cond. Prob
Independent Events
Real World Cond. Prob
Cond. Prob. Pitfalls
Unit 2: Bayes' Theorem
Intro to Bayes' Theorem
Applying Bayes' Theorem
Bayes' Theorem Examples
Prior Probabilities
Bayes' vs Frequentist
Unit 3: Advanced Applications of Bayes' Theorem
Bayesian Inference
Bayesian Networks
Naive Bayes Classifiers
Hierarchical Bayes
Bayes in Data Science
Discrete Random Variables and Distributions
Unit 1: Introduction to Discrete Random Variables
What are Random Variables?
Probability Mass Function
Cumulative Distribution
Expected Value
Variance and Deviation
Unit 2: Bernoulli and Binomial Distributions
Bernoulli Distribution
Binomial Distribution
Mean of Binomial Dist.
Variance of Binomial
Binomial Examples
Unit 3: Poisson and Geometric Distributions
Poisson Distribution
Mean of Poisson Dist.
Variance of Poisson
Geometric Distribution
Geometric Examples
Continuous Random Variables and Distributions
Unit 1: Introduction to Continuous Random Variables
Continuous Variables
Probability Density
Cumulative Distribution
Mean and Variance
Applications of PDFs
Unit 2: Uniform Distribution
Uniform Distribution
PDF of Uniform Dist.
CDF of Uniform Dist.
Mean & Variance
Uniform Applications
Unit 3: Exponential Distribution
Exponential Intro
PDF of Exponential
CDF of Exponential
Memoryless Property
Applications
Unit 4: Normal Distribution
Normal Distribution
PDF of Normal
Standard Normal Dist.
Using Z-Tables
Normal Applications
Applications of Probability and Expected Value
Unit 1: Probability in Machine Learning
Prob. in Classification
Prob. in Regression
Naive Bayes Explained
Logistic Regression
ML Model Evaluation
Unit 2: Probability in AI and Expert Systems
Prob. in Expert Sys.
Bayesian Networks
Prob. Reasoning
Markov Decision Proc.
AI Prob. Challenges
Unit 3: Probability in Risk Management
Risk Identification
Risk Assessment
Risk Mitigation
Decision Making
Case Study