# Universality of the uniform

2021 May 19 See all posts

## Universality

Given $U$ uniformly distributed over $(0,1)$, and $X$ with CDF $F$

$F^{-1}(U) = X$ and $F(X) = U$

Visually

## TODO

1. Briefly explain random variables, probability distributions with examples
2. Explain the uniform distribution
3. Show transformations on the uniform CDFs
4. Show with the PDFs