[[Uniform distribution]]
# Universality of the uniform distribution

Let $Y \sim \mathrm{U}(0,1)$,
$F$ be the [[cumulative distribution function]] of a [[real random variable]] $X : \xi \to \mathbb{R}$,
and $F^{-1}$ be the corresponding [[Quantile function]].
Then #m/thm/prob
$$
\begin{align*}
F(X) &\sim Y \\
X &\sim F^{-1}(Y)
\end{align*}
$$

> [!missing]- Proof
> #missing/proof

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