> ## Documentation Index
> Fetch the complete documentation index at: https://math.aboneda.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Overview

> Foundations of probability theory

# Probability

Probability is the branch of mathematics that studies the likelihood of events occurring. It provides the mathematical framework for quantifying uncertainty and reasoning about random phenomena.

## Key Topics

* **Sample Spaces & Events** — defining the set of all possible outcomes
* **Axioms of Probability** — Kolmogorov's foundational axioms
* **Conditional Probability** — P(A|B) and updating beliefs with new information
* **Bayes' Theorem** — reversing conditional probabilities
* **Random Variables** — discrete and continuous
* **Distributions** — Binomial, Poisson, Normal, Exponential, and more
* **Expectation & Variance** — summarizing distributions
* **Law of Large Numbers & Central Limit Theorem** — convergence results

## we will be taking it from these resources

1. [Steven Brunton - Probability Bootcamp](https://www.youtube.com/watch?v=sQqniayndb4\&list=PLMrJAkhIeNNR3sNYvfgiKgcStwuPSts9V)
2. [ROSS - Book](https://chengzhaoxi.xyz/download/pdf/book/A-First-Course-in-Probability.pdf)
3. [mathematicalmonk - Probability Primer series](https://www.youtube.com/watch?v=Tk4ubu7BlSk\&list=PL17567A1A3F5DB5E4)
4. [J.K Blitzstein - Book](https://uni.dcdev.ro/y2s2/ps/Introduction%20to%20Probability%20by%20Joseph%20K.%20Blitzstein,%20Jessica%20Hwang%20\(z-lib.org\).pdf)
5. [One Video](https://www.youtube.com/watch?v=HcdimX9ULHQ)
6. [Tübingen Machine Learning - Course](https://www.youtube.com/watch?v=TTo2kjrAuTo\&list=PL05umP7R6ij2YE8rRJSb-olDNbntAQ_Bx)
7. [CodeEmporium - Probability Theory for ML](https://www.youtube.com/watch?v=zrd8KujWxKw\&list=PLTl9hO2Oobd9bPcq0fj91Jgk_-h1H_W3V)
8. [Stanford - Probability for Computer Scientists](https://www.youtube.com/watch?v=2MuDZIAzBMY\&list=PLoROMvodv4rOpr_A7B9SriE_iZmkanvUg)
9. [Distributions](https://www.youtube.com/watch?v=YXLVjCKVP7U\&list=PLTNMv857s9WVzutwxaMb0YZKW7hoveGLS)
10. [statlect Probability](https://www.statlect.com/fundamentals-of-probability/)
11. [probabilitycourse](https://www.probabilitycourse.com/)