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Convolutions | Why X+Y in probability is a beautiful mess

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3Blue1Brown

Adding random variables, with connections to the central limit theorem.
Help fund future projects:   / 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, flipandslide
8:41 The discrete formula
10:58 Continuous case, flipandslide
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: @DavidBarOn, David BarOn, Omer Tuchfeld
Spanish: Derek Lacayo



These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim'>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  
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Patreon:   / 3blue1brown  
Facebook:   / 3blue1brown  

posted by Hemme1v