# Universality of the uniform

2021 May 19
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## Universality

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

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

Visually

## TODO

- Briefly explain random variables, probability distributions with examples
- Explain the uniform distribution
- Show transformations on the uniform CDFs
- Show with the PDFs