## TL;DR
Statistics provides the mathematical framework for drawing conclusions from data. Probability quantifies uncertainty; hypothesis testing evaluates evidence; regression models relationships. The Bayesian-frequentist debate reflects two valid philosophies of inference.

## Core Explanation
Descriptive statistics: mean, median, variance, correlation. Probability distributions: normal (Gaussian), binomial, Poisson, exponential. Central Limit Theorem: sample means approach normality as n increases. Hypothesis testing: null vs alternative, Type I (false positive) and Type II (false negative) errors.

## Detailed Analysis
Regression: linear (OLS), logistic (binary outcomes), multilevel/hierarchical. Multiple testing correction: Bonferroni, False Discovery Rate (Benjamini-Hochberg). Bayesian approach: prior → likelihood → posterior. Markov Chain Monte Carlo (MCMC) enables computation for complex models.

## Further Reading
- OpenIntro Statistics (free textbook)
- MIT 18.05: Probability and Statistics
- Statistical Rethinking (McElreath)