<aside> 📌 "God does not play dice with the universe." - Albert Einstein
</aside>
Chapter 1**: Introduction to Probability**
Chapter 2: Discrete Probability Distributions
Appendix B: Monte Carlo and Estimating Integrals
1.1 Experiments, Outcomes, and Events 1.2 Probability Definitions 1.3 Probability Axioms 1.4 Probability of Union of Events and Union Bound 1.5 Probability of Intersection of Events and Independence 1.6 Conditional Probability 1.7 Law of Total Probability 1.8 Bayes' Rule
Chapter 2: Discrete Probability Distributions 2.1 Discrete Random Variables 2.2 Probability Mass Function (PMF) 2.3 Cumulative Distribution Function (CDF) 2.4 Common Discrete Probability Distributions 2.5 Python Implementation and Visualization 2.6 Solving Problems with Discrete Distributions
Chapter 3: Continuous Probability Distributions 3.1 Continuous Random Variables 3.2 Probability Density Function (PDF) 3.3 Cumulative Distribution Function (CDF) 3.4 Common Continuous Probability Distributions 3.5 Python Implementation and Visualization 3.6 Solving Problems with Continuous Distributions
Chapter 4: Expectations and Moments 4.1 Mean, Variance, and Standard Deviation 4.2 Higher Moments 4.3 Moment Generating Function 4.4 Python Exercises for Computing Expectations, Variances, and Moments
Chapter 5: The Law of Large Numbers 5.1 The Weak Law of Large Numbers 5.2 Convergence in Probability 5.3 Python Demonstrations 5.4 Conclusion
Chapter 6: The Central Limit Theorem 6.1 The Central Limit Theorem 6.2 Python Demonstrations 6.3 Conclusion
Chapter 7: Confidence Intervals 7.1 Basics of Confidence Intervals 7.2 Types of Errors and Significance Levels 7.3 Gaussian (Normal) Confidence Interval 7.4 t-Student Confidence Interval 7.5 Choosing between Gaussian and t-Student Confidence Intervals
Chapter 8: Regression and Correlation 8.1 Introduction to Linear Regression 8.2 Correlation Coefficients 8.3 Implementing Regression Analysis in Python 8.4 Interpreting the Results 8.5 Conclusion
Chapter 9: Monte Carlo Simulations 9.1 Principles of Monte Carlo Simulations 9.2 Python Examples for Practical Applications 9.3 Conclusion