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Assume there are n points randomly distributed in a rectangle (x being the height y being the width) shown below in the figure.

enter image description here

I would like to calculate the average distance between 2 random red points, but my constraints are that these red points are cannot be distributed in the blue and grey colored area. (Areas are 3a * a, 7a * a for blue and grey respectively.)

There are 6 grey colored areas and 4 blue colored areas.

Assuming that the red points are randomly distributed in this rectangle expect for the blue& grey colored areas, what is the average distance between these red points??

I know that this is quite narrow cased, but what would be the mathematical calculations for this?

I would appreciate some help.

Yun Hyunsoo
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    To get a sense of the calculations needed even in the simplest case of a rectangle (with no obstacles), see https://stats.stackexchange.com/a/52931/919. This should convince you that the best practical solution to your question is a simulation. To get an exact solution, you need a (slight) generalization that computes the expected distance between one rectangle and a different (isothetic) rectangle, and then a little algebra (of mixtures) will give you the solution. – whuber Jan 05 '21 at 15:25

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