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Distribution of n*min(u1,u2)

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Let [itex]{U_k}_{k \in \mathbb{N}}[/itex] be i.i.d from the uniform (0,1) distribution.
    I need a formula for the cumulative distribution function of [itex]X_n[/itex], defined as
    [itex]X_n := n* \min(U_1, \ldots ,U_n)[/itex]

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

    [itex]*[/itex] is meant to be multiplication..

    2. Relevant equations



    3. The attempt at a solution
    Know already that [itex]P(min(U_1, \ldots ,U_n) \leq x) = 1 - (1-x)^n[/itex]
     
    Last edited: Oct 9, 2012
  2. jcsd
  3. Oct 9, 2012 #2
    Sorry to bump this thread,but I still haven't figured it out. Does anyone know how to find it?
     
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