Why the "central limit" is a normal distribution
Added 2023-07-10 18:49:28 +0000 UTCHere's an early view for the next video, capping off the mini-series about normal distributions. I have just one to-do stub left in there for myself, but let me know if you catch anything else that should change before the final release.
Comments
Differential entropy is just the continuous analogue of discrete entropy.
Daksha Vaid-Kwinter
2023-08-10 14:31:35 +0000 UTCHey Grant! I think it'd be super interesting to see a video/series on discrete calculus (so many mathematics majors never get to see the intricacy and beauty of it!) and use the connections with continuous calculus to give intuition for the binomial approximation of the normal distribution. Just some food for thought for a different angle to approach!
Stuart Jones
2023-07-23 13:27:24 +0000 UTCI had been meaning to try to create a proof of CLT based on the intuition that convolution increases entropy "faster" than variance, and Gaussians maximize entropy for a given variance. Partly I was frustrated that most justifications of the Gaussian distribution go to two dimensions, and it seems like that shouldn't be necessary. Interesting to hear that this is a standard argument, although apparently it uses something called "differential entropy" and I don't know what that is.
Craig Falls
2023-07-13 23:25:24 +0000 UTCCorrection: https://www.youtube.com/watch?v=d_qvLDhkg00 9 minutes 3 seconds https://www.youtube.com/watch?v=d_qvLDhkg00&t=9m3s right side second word: transformatoin -> transformation
Thomas Schneider
2023-07-11 21:26:42 +0000 UTC
