2023-06-27

[public] 178K views, 23.4K likes, dislikes audio only

3Blue1Brown

Adding random variables, with connections to the central limit theorem.

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

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

0:00 - Intro quiz

2:24 - Discrete case, diagonal slices

6:49 - Discrete case, flip-and-slide

8:41 - The discrete formula

10:58 - Continuous case, flip-and-slide

15:53 - Example with uniform distributions

18:42 - Central limit theorem

20:50 - Continuous case, diagonal slices

25:26 - Returning to the intro quiz

Thanks to these viewers for their contributions to translations

Hebrew: @DavidBar-On, David Bar-On, Omer Tuchfeld

Spanish: Derek Lacayo

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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