2023-07-11

[public] 192K views, 21.8K likes, dislikes audio only

3Blue1Brown

A visual trick to compute the sum of two normally distributed variables.

3b1b mailing list: https://3blue1brown.substack.com/

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

Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-convolution#thanks

For the technically curious who want to go deeper, here's a proof of the central limit theorem using Moment generating functions:

https://www.cs.toronto.edu/~yuvalf/CLT.pdf

And here's a nice discussion of methods using entropy:

https://mathoverflow.net/questions/182752/central-limit-theorem-via-maximal-entropy

Relevant previous videos

Central limit theorem

/youtube/video/zeJD6dqJ5lo

Why π is there, and the Herschel-Maxwell derivation

/youtube/video/cy8r7WSuT1I

Convolutions and adding random variables

/youtube/video/IaSGqQa5O-M

Time stamps

0:00 - Recap on where we are

2:10 - What direct calculation would look like

3:38 - The visual trick

8:27 - How this fits into the Central Limit Theorem

12:30 - Mailing list

Thanks to these viewers for their contributions to translations

German: lprecord, qoheniac

Spanish: Pablo Asenjo Navas-Parejo

Vietnamese: Duy Tran

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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