$N$ points are generated randomly within a unit square, with a uniform distribution. What is the probability that the points form a connected graph, given that two points are connected if the distance between them is less than or equal to $d$? (this should obviously be some function of $N$ and $d$).
If you don't know the answer, but have an idea that may (or may not) lead me a step forward, please let me know as well.
Moreover, if you know for sure that this problem is yet unsolved, that's also good news for me. I can then do it through a Monte-Carlo simulation, but my approach would be justified.