.. _chapter1:

Chapter 1: Statistical Paradigms and Core Concepts
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.. contents:: Chapter Contents
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   :depth: 2

This chapter establishes the foundation for computational data science by covering three essential topics:

1. **Probability foundations and inference paradigms** (Section 1.1): Kolmogorov's axioms and 
   philosophical interpretations of probability; comparison of frequentist, Bayesian, and 
   likelihood-based inference approaches

2. **Probability distributions** (Section 1.2): Comprehensive review of discrete and continuous 
   distributions, their properties, relationships, and applications; detailed treatment of PMFs, 
   PDFs, and CDFs

3. **Python random generation** (Section 1.3): Practical implementation of probability concepts 
   using Python's ecosystem (random, NumPy, SciPy)

**Learning Objectives:** Upon completion of this chapter, students will be able to:

* Understand Kolmogorov's axiomatic foundation of probability
* Explore different interpretations of what probability means (frequentist, Bayesian, propensity)
* Compare major statistical inference paradigms (Frequentist, Bayesian, Likelihoodist)
* Recognize philosophical debates and practical trade-offs between approaches
* Work fluently with random variables, PMFs, PDFs, and CDFs
* Understand key properties and applications of major probability distributions
* Generate random samples from various distributions using Python
* Compute probabilities, quantiles, and other distribution properties
* Choose appropriate Python library and distribution for specific problems

.. toctree::
   :maxdepth: 2
   :caption: Sections

   ch1.1-probability-and-inference-paradigms
   ch1.2-probability_distributions_review
   ch1.3-python_random_generation
   ch1.4-chapter-summary