A pretty reason why Gaussian + Gaussian = Gaussian
A visual trick to compute the sum of two normally distributed variables.
3b1b mailing list: https://3blue1brown.substack.com/
Help fund future projects: / 3blue1brown
Special thanks to these supporters: https://www.3blue1brown.com/lessons/g...
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/CL...
And here's a nice discussion of methods using entropy:
https://mathoverflow.net/questions/18...
Relevant previous videos
Central limit theorem
• But what is the Central Limit Theorem?
Why π is there, and the Herschel-Maxwell derivation
• Why π is in the normal distribution (...
Convolutions and adding random variables
• Convolutions | Why X+Y in probability...
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
------------------
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/a...
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...
------------------
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: / 3blue1brown
Reddit: / 3blue1brown
Instagram: / 3blue1brown
Patreon: / 3blue1brown
Facebook: / 3blue1brown
