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
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
https://youtu.be/zeJD6dqJ5lo
Why π is there, and the Herschel-Maxwell derivation
https://youtu.be/cy8r7WSuT1I
Convolutions and adding random variables
https://youtu.be/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
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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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