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

Adding random variables, with connections to the central limit theorem.
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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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github.com/3b1b/manim
github.com/ManimCommunity/manim/

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Music by Vincent Rubinetti.
www.vincentrubinetti.com/

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