2023-03-14

[public] 431K views, 65.0K likes, dislikes audio only

3Blue1Brown

A visual introduction to probability's most important theorem

Help fund future projects: https://www.patreon.com/3blue1brown

Special thanks to these lovely supporters: https://www.3blue1brown.com/lessons/clt#thanks

An equally valuable form of support is to simply share the videos.

Galton board shown in the video: https://amzn.to/3ZJK8nY

Thanks to these viewers for their contributions to translations

Hebrew: David Bar-On, Omer Tuchfeld

Hindi: Tapender1

Italian: anna-lombardo

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Timestamps

0:00 - Introduction

1:53 - A simplified Galton Board

4:14 - The general idea

6:15 - Dice simulations

8:55 - The true distributions for sums

11:41 - Mean, variance, and standard deviation

15:54 - Unpacking the Gaussian formula

20:47 - The more elegant formulation

25:01 - A concrete example

27:10 - Sample means

28:10 - Underlying assumptions

Correction: 6:37 The narration should say "skewed left"

Correction: 7:15 Again, the narration should say "skews a tiny bit left"

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These animations are largely made using a custom python library, manim. See the FAQ comments here:

https://www.3blue1brown.com/faq#manim

https://github.com/3b1b/manim

https://github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:

https://github.com/3b1b/videos/

Music by Vincent Rubinetti.

https://www.vincentrubinetti.com/

Download the music on Bandcamp:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:

Website: https://www.3blue1brown.com

Twitter: https://twitter.com/3blue1brown

Reddit: https://www.reddit.com/r/3blue1brown

Instagram: https://www.instagram.com/3blue1brown

Patreon: https://patreon.com/3blue1brown

Facebook: https://www.facebook.com/3blue1brown