Newsletter #6 - Central Limit Theorem

Learning resources for the Central Limit Theorem, a key theorem in probability and statistics.

Welcome to the sixth issue of the Aleph 0 newsletter! This issue, we’re covering the Central Limit Theorem, one of the key theorems in probability and statistics.

Learning Resources

This week’s topic is the central limit theorem. Roughly speaking, the central limit theorem says that if you take large enough samples from a population, the means of the samples will be normally distributed (i.e: they will be shaped like a bell curve). This is true even if the original population isn’t normally distributed.

Here are some resources to learn the subject:

1. Here is a video by 3b1b (Grant Sanderson) explaining the Central Limit Theorem in a very intuitive and visual way:

2. Here is another video by Khan Academy about the central limit theorem. I watched this when I was first learning about the concept, and I found the explanation very clear!

Challenge Problem

There are 2000 points on a circle, and each point is given a number that is equal to the average of the numbers of its two nearest neighbors. Show that all the numbers must be equal.

If you have a solution to the above challenge problem, submit it here for a chance to be featured in the next issue of this newsletter.

Solution from last week

See here for the solution to last week’s problem. (Shoutout to Ritoprovo Roy from Budapest whose solution is being featured this week!)

Feedback

If you have any learning resources that you think would be valuable for readers, or if you have any general feedback, let me know here and I’d be happy to incorporate it.

Thanks for reading and happy learning! Until next time,

Adithya