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But what is the Central Limit Theorem?

3Blue1Brown
7.55M subscribers
4M views 2 years ago
A visual introduction to probability's most important theorem Help fund future projects:   / 3blue1brown   Special thanks to these lovely supporters: https://www.3blue1brown.com/lessons/c... An equally valuable form of support is to simply share the videos. Galton board shown in the video: https://amzn.to/3ZJK8nY Thanks to these viewers for their contributions to translations Hebrew: David Bar-On, Omer Tuchfeld Hindi: Tapender1 Italian: anna-lombardo ----------------- Timestamps 0:00 - Introduction 1:53 - A simplified Galton Board 4:14 - The general idea 6:15 - Dice simulations 8:55 - The true distributions for sums 11:41 - Mean, variance, and standard deviation 15:54 - Unpacking the Gaussian formula 20:47 - The more elegant formulation 25:01 - A concrete example 27:10 - Sample means 28:10 - Underlying assumptions Correction: 6:37 The narration should say "skewed left" Correction: 7:15 Again, the narration should say "skews a tiny bit left" …...more
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But what is the Central Limit Theorem?
75KLikes
4,069,309Views
2023Mar 14
A visual introduction to probability's most important theorem Help fund future projects:   / 3blue1brown   Special thanks to these lovely supporters: https://www.3blue1brown.com/lessons/c... An equally valuable form of support is to simply share the videos. Galton board shown in the video: https://amzn.to/3ZJK8nY Thanks to these viewers for their contributions to translations Hebrew: David Bar-On, Omer Tuchfeld Hindi: Tapender1 Italian: anna-lombardo ----------------- Timestamps 0:00 - Introduction 1:53 - A simplified Galton Board 4:14 - The general idea 6:15 - Dice simulations 8:55 - The true distributions for sums 11:41 - Mean, variance, and standard deviation 15:54 - Unpacking the Gaussian formula 20:47 - The more elegant formulation 25:01 - A concrete example 27:10 - Sample means 28:10 - Underlying assumptions Correction: 6:37 The narration should say "skewed left" Correction: 7:15 Again, the narration should say "skews a tiny bit left" ------------------ 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/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   Instagram:   / 3blue1brown   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown  

Follow along using the transcript.

3Blue1Brown

7.55M subscribers