How to visualize joint uniform distribution

  • #1

Main Question or Discussion Point

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:
 

Answers and Replies

  • #2
EnumaElish
Science Advisor
Homework Helper
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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.
 
  • #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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