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A quick Question on Joint Uniform Distribution

  1. Aug 19, 2015 #1
    Hi, I have a quick question.

    If both X and Y are uniformly distributed on the unit interval [0, 1]. Can we prove that the joint distribution of (X, Y) is uniform on the unit square [0, 1]×[0, 1]? Do we need any condition to ensure the result, such as Independence between X and Y?

    Thanks.
     
  2. jcsd
  3. Aug 19, 2015 #2

    Orodruin

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    Yes, you do need independence. Consider the case X = Y, the resulting distribution is along the diagonal.
     
  4. Aug 20, 2015 #3
    Thanks.
     
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