Consider a Poisson Boolean Process (X,$\lambda$,1) where $\lambda>0$ is the Poisson intensity of a two dimensional Poisson process. The Boolean process is such that at the center of each Poisson point a square tile is centered with side 1. (Usually the process uses balls instead of squares. But that's a minor difference).
Given the unit square $I^2$ in the plain, does somebody know what the (coverage) probability is that the unit square is covered by the random tiles as a function of $\lambda$. I heared from my professor that there is an article on the coverage probability of more general areas in the plain by such processes. But I can't seem to find it. If somebody knows of it, please let me know.
Kindly appreciated,
Aris
