2D Normal Distributions

About this lesson

⏭️ 𝘾𝙤𝙣𝙣𝙚𝙘𝙩 𝙬𝙞𝙩𝙝 𝙪𝙨 𝙤𝙣 𝙋𝘼𝙏𝙍𝙀𝙊𝙉 https://www.patreon.com/socratica We've discussed the one-dimensional Normal Distribution (the bell curve) in a previous video, so you're all experts now! Normal Distributions https://youtu.be/xlxaa9YhT6A In this lesson, we extend the familiar Bell Curve into two dimensions. The 2D normal distribution — also called the Gaussian distribution in two variables — describes how data spreads when there’s variation in two directions at once. Starting with darts on a board and lengths of wood, we build up the intuition for moving from 1D to 2D. You’ll learn how the mean vector and covariance matrix define the shape of the distribution, and how probability density functions generalize from curves to surfaces. Along the way, we explore real-world applications, including stock market returns and precision sports. By the end, you’ll see how the 2D case prepares us for the general multivariate normal distribution in any number of dimensions ⏭️ 𝙔𝙤𝙪 𝙘𝙖𝙣 𝙟𝙪𝙢𝙥 𝙩𝙤 𝙨𝙚𝙘𝙩𝙞𝙤𝙣𝙨 𝙤𝙛 𝙩𝙝𝙚 𝙫𝙞𝙙𝙚𝙤 𝙝𝙚𝙧𝙚: 0:00 Darts and 2D variation 1:00 Recap of 1D normal distributions 2:00 From curves to surfaces 3:00 The mean vector 4:30 The covariance matrix 6:00 Stock returns example 7:30 The 2D probability density function 9:00 Applications: darts & stocks 11:00 From 2D to N-dimensional distributions ▶️ 𝙒𝘼𝙏𝘾𝙃 𝙉𝙀𝙓𝙏: Normal Distributions https://youtu.be/xlxaa9YhT6A Special thanks to our wonderful Patreon supporters: Umar Khan Tracy Karin Prell Thomas Myers Michael Shebanow Marcos Silveira M Andrews KW Kevin B John Krawiec Jeremy Shimanek Eric Eccleston Christopher Kemsley Jim Woodworth Thank you, kind friends! 💜🦉 𝘽𝙚𝙘𝙤𝙢𝙚 𝙤𝙪𝙧 𝙋𝙖𝙩𝙧𝙤𝙣 𝙤𝙣 𝙋𝙖𝙩𝙧𝙚𝙤𝙣: https://www.patreon.com/socratica 📚 𝙒𝙚 𝙧𝙚𝙘𝙤𝙢𝙢𝙚𝙣𝙙 (affiliate links): The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow https://amzn.to/4j9n0YP The Art of Statistics: How to Learn from Data by David Spiegelha

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