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Distribution function of 2D random vector

  1. Mar 2, 2010 #1
    1. The problem statement, all variables and given/known data
    Write the distribution function of the 2D random vector which is uniformly distributed in the triangle with the corners {(0,0),(0,1),(1,0)}.

    2. Relevant equations
    [tex]F_{X,Y} (x,y) = Pr(X \le x, Y \le y)[/tex]

    3. The attempt at a solution
    Sorry, but I don't know even where to start. I guess the vector is (X,Y), where X and Y are the coordinates of the "head" of the vector. The vector is uniformly distributed among the triangle area, but X and Y are not uniformly distributed between [0,1]. I don't know how to express the relation between them nor how to continue.

    Solution
    http://img696.imageshack.us/img696/663/screenshotow.png [Broken]
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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