# Distribution of n*min(u1,u2)

1. Oct 9, 2012

### infk

1. The problem statement, all variables and given/known data
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..

2. Relevant equations

3. The attempt at a solution
Know already that $P(min(U_1, \ldots ,U_n) \leq x) = 1 - (1-x)^n$

Last edited: Oct 9, 2012
2. Oct 9, 2012

### infk

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