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Finding minimum variable's density function

  1. Sep 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Let X and Y be independent and suppose that each has a Uniform (0,10) distribution.
    Let Z = min{X, Y }. Find the density fZ(z) for Z.


    2. Relevant equations



    3. The attempt at a solution
    i'm sorry but i really don't know how to handle this.
     
  2. jcsd
  3. Sep 11, 2014 #2

    haruspex

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    Start by finding the cdf.
     
  4. Sep 11, 2014 #3
    if x and y both have same uniform distribution, then z has the same distribution as x and y?
     
  5. Sep 11, 2014 #4

    Ray Vickson

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    What are your reasons for thinking this? Have you actually computed the distribution?
     
  6. Sep 11, 2014 #5

    haruspex

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    FX(x) is the probability of what? Likewise, FZ(z).
     
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