If X, Y ~ N(0,1), then X/Y ~ Cauchy(0,1) (Read: If X and Y are normally distributed random variables with mean 0 and standard deviation 1, then X/Y is equivale

If X, Y ~ N(0,1), then X/Y ~ Cauchy(0,1) (Read: If X and Y are normally distributed random variables with mean 0 and standard deviation 1, then X/Y is equivalent to a Cauchy(0,1) distributed RV. This is a useful equivalence to know if working with standard normal RVs, which is often. E[X/Y] does not exist!) If X ~ Cauchy(0,1), then X ~ normalized student-t distribution. (student-t puts the “t” in t-SNE, where it acts as a weighting function on the Euclidean distance between points. UMAP uses a parameterized version of this weight function that is essentially a generalization of the Cauchy distribution: https://jlmelville.github.io/smallvis/umap.html https://jlmelville.github.io/smallvis/umap.html)