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: 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 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 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/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 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
