Table of Contents
Preface
Chapter 1: Probability Foundations
- Introduction
- Basic Definitions
- Axioms of Probability
- Addition Rule
- Conditional Probability
- Independence
- Law of Total Probability
- Bayes' Theorem
- ML Insight
- Quick Summary
Chapter 2: Probability Distributions
- Introduction
- Discrete vs Continuous Distributions
- Bernoulli Distribution
- Binomial Distribution
- Poisson Distribution
- Uniform Distribution
- Normal Distribution
- Exponential Distribution
- When to Use Which Distribution
- Interview Questions and Tricks
- Quick Summary
Chapter 3: Descriptive Statistics
- Introduction
- Measures of Central Tendency
- Mean
- Median
- Mode
- Measures of Dispersion
- Variance
- Standard Deviation
- Skewness
- Kurtosis
- Range and IQR
- Outlier Detection
- Z-Score
- Interview Questions and Tricks
- Quick Summary
Chapter 4: Maximum Likelihood Estimation (MLE)
- Introduction
- Basic Idea of MLE
- Log-Likelihood
- MLE for Bernoulli Distribution
- MLE for Normal Distribution
- Steps to Compute MLE
- Examples
- MLE in Machine Learning
- MLE vs MAP
- Interview Questions and Tricks
- Common Mistakes
- Quick Summary
Chapter 5: Bayesian Inference
- Introduction
- Bayes' Theorem
- Prior, Likelihood, Posterior
- Example: Medical Testing
- Maximum A Posteriori (MAP)
- Conjugate Priors
- Bayesian Updating
- Python Example
- Bayesian in Machine Learning
- Interview Questions and Tricks
- Common Mistakes
- Quick Summary
Chapter 6: Hypothesis Testing
- Introduction
- Basic Concepts
- Type I and Type II Errors
- p-value
- Z-Test
- t-Test
- Chi-Square Test
- ANOVA
- One-Tailed vs Two-Tailed Tests
- Hypothesis Testing in ML
- Interview Questions and Tricks
- Common Mistakes
- Quick Summary
Chapter 7: Linear Algebra for Statistics
- Vectors and Matrices
- Covariance Matrix
- Correlation
- Eigenvalues and Eigenvectors
- ML Applications
Chapter 8: Information Theory
- Entropy
- Cross-Entropy
- KL Divergence
- ML Applications
Chapter 9: Model Evaluation
- Bias vs Variance
- Cross-Validation
- Accuracy, Precision, Recall
- F1 Score
- ML Metrics
Appendix
- Python Code Reference
- Formula Cheat Sheet