Adding random variables, with connections to the central limit theorem. Help fund future projects: https://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 ------------------ 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