From Statistics Libre Text:
For samples of size 30 or more, the sample mean is approximately normally distributed, with mean μX = μ and standard deviation σX = σ/√n where n is the sample size. The larger the sample size, the better the approximation.
The above is a pretty typical assertion in statistics texts. The derivation must be a doozy, it’s never shown, and there’s rarely a discussion of the Central Limit Theory itself.
I read an article about Term Frequency-Inverse Document Frequency on John D. Cook Consulting’s blog.
It is said that the Fibonacci Sequence appears all over the place in nature.
In 2020, when one particular political faction created a controversy by claiming that national elections might be rigged, I decided to check into how my state, Colorado, audited the results of elections.
From the Wikipedia article on Cauchy distributions:
When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U / V has the standard Cauchy distribution.
Since I’m limbered up by making linear combinations of Cauchy distributions, I feel like this one is easy.
Edit 2025-07-20: Dr Drang mentioned this post! He did an analytical solution and found my curve fit wanting! That’s cool, I violated the assumptions, so it should be wrong!
Wikipedia says, about stable distributions:
a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters.
Here’s a 70 year old paper that’s worth a closer look:
Leo A. Goodman (1954) Some Practical Techniques in Serial Number Analysis, Journal of the American Statistical Association, 49:265, 97-112
I take Pepcid Complete chewable tablets for heartburn.
I bought a couple of 10mm cubes, one of Nickel, one of Cobalt, because I read that cobalt and nickel are ferromagnetic, strongly attracted to magnets. I could not distinguish the two cubes based on density. I’m documenting my effort to distinguish them based on magnetic attraction.
My son, Everett, helped me with experiment design and execution.
Found a puzzle on the notorious Futility Closet web site.
Here’s Futility Closet’s puzzle. Mr or Ms Closet decided to call the puzzle “Gun Control”. I don’t know if they chose the title to skirt controversy or something.
Problem Statement
Marksman A hits a certain small target 75 percent of the time. Marksman B hits it 25 percent of the time. The two of them aim at that target and fire simultaneously. One bullet hits it. What’s the probability that it came from A?
