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

Adding random variables, with connections to the central limit theorem.
Help fund future projects: www.patreon.com/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, flip-and-slide
8:41 - The discrete formula
10:58 - Continuous case, flip-and-slide
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: @DavidBar-On, David Bar-On, Omer Tuchfeld
Spanish: Derek Lacayo

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These animations are largely made using a custom python library, manim. See the FAQ comments here:
www.3blue1brown.com/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:
github.com/3b1b/videos/

Music by Vincent Rubinetti.
www.vincentrubinetti.com/

Download the music on Bandcamp:
vincerubinetti.bandcamp.com/album/the-music-of-3bl…

Stream the music on Spotify:
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: 3b1b.co/subscribe

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