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How to visualize joint uniform distribution

  1. Sep 2, 2005 #1
    Lets say you have X and Y, where the joint density function for X and Y is uniform over the region defined by 0<=x<=y<=L, where L is some positive constant.

    The question asks for the expected value of the squares of X and Y.

    I am having trouble visualizing what such a distribution would look like. Apparently it is triangular shaped... but I do not see it. Can anyone help?

    Thanks in advance...
    :confused:
     
  2. jcsd
  3. Sep 3, 2005 #2

    EnumaElish

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    Suppose L = 1. Then the distribution is defined over the triangle above the y = x line in the unit square. The frequency is marked on the Z axis and is constant over the whole triangular area. So, you have a triangular prism; its volume = 1 by definition.
     
  4. Sep 4, 2005 #3
    just integrate,
    you will get:
    [tex]E[X^2]=L^2/6[/tex]
    [tex]E[Y^2]=L^2/2[/tex]
     
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