What Is the Distribution of \( n \times \min(U_1, \dots, U_n) \)?

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Homework Statement

Let ${U_k}_{k \in \mathbb{N}}$ be i.i.d from the uniform (0,1) distribution.
I need a formula for the cumulative distribution function of $X_n$, defined as
$X_n := n* \min(U_1, \ldots ,U_n)$

Also some advice for $X_n := \sqrt{n}* \min(U_1, \ldots ,U_n)$ would be appreciated.

$*$ is meant to be multiplication..

Homework Equations

The Attempt at a Solution

Know already that $P(min(U_1, \ldots ,U_n) \leq x) = 1 - (1-x)^n$

 

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Sorry to bump this thread,but I still haven't figured it out. Does anyone know how to find it?