# How to visualize joint uniform distribution

1. Sep 2, 2005

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?

2. Sep 3, 2005

### EnumaElish

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. Sep 4, 2005

### balakrishnan_v

just integrate,
you will get:
$$E[X^2]=L^2/6$$
$$E[Y^2]=L^2/2$$