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?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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