# Thread: CDF of distance between two points on a bounded line-segment.

1. ## CDF of distance between two points on a bounded line-segment.

Hi all,

I am trying to solve a paper, and I cannot understand (especially geometrically) how the limits
are applied while finding CDF for the distance between two points (I understand how they are calculating CDF, but my point is
how they have find the limits involved.). The question is attached as a figure.

2. ## Re: CDF of distance between two points on a bounded line-segment.

see if this drawing helps

3. ## Re: CDF of distance between two points on a bounded line-segment.

Originally Posted by romsek
see if this drawing helps

Thanks for your message. However, some numerical help will be much appreciated. (note that my question is related to line segment only, not a rectangle!)

4. ## Re: CDF of distance between two points on a bounded line-segment.

Originally Posted by sjaffry
Thanks for your message. However, some numerical help will be much appreciated. (note that my question is related to line segment only, not a rectangle!)
you have a 2D joint distribution you are integrating over. The colored area is the total area of integration for $|x_1 - x_2|<\lambda$

The three different colors represent the areas of integration corresponding to the three integrals in the highlighted area of the paper.

Look a little harder, it's not that hard.