🎰 Introduction to Probability

If a paper page uses distributions, expectations, or Markov chains and you want the ground-level definitions, start here.

	Chapter
1.	Discrete Probability	Sample spaces, events, and assigning probabilities to outcomes you can count	🎰
2.	Continuous Probability	When outcomes are real numbers, probabilities are areas under curves	🎰
3.	Combinatorics	Counting arrangements: permutations, combinations, binomial coefficients	🎰
4.	Conditional Probability	P(A\|B) = P(A and B) / P(B), and why Bayes' theorem follows	🎰
5.	Distributions	Binomial, Poisson, geometric, normal: the named distributions and when they arise	🎰
6.	Expected Value	The weighted average of outcomes, and variance as spread around it	🎰
7.	Sums of Random Variables	Add independent random variables: means add, variances add, distributions convolve	🎰
8.	Law of Large Numbers	Averages converge to the expected value as sample size grows	🎰
9.	Central Limit Theorem	Sums of many independent variables approach a normal distribution	🎰
10.	Generating Functions	Encode a distribution as a polynomial, then multiply polynomials to convolve	🎰
11.	Markov Chains	Memoryless state machines: the next state depends only on the current one	🎰
12.	Random Walks	Step left or right with equal probability: will you return to the origin?	🎰

Neighbors

📊 Statistics — probability distributions reappear as inference tools
📡 Information Theory — entropy is expected surprise over a probability distribution
🤖 Machine Learning — Bayesian models, Gaussian processes, and sampling
🎲 Game Theory — mixed strategies are probability distributions over actions