Finite random geometric graphs are often constructed by randomly picking points in a square, assigning nodes to these points, and assigning edges between nodes if circles of radius r around each node cover another node.
In this scenario the expected number of isolated nodes is (https://arxiv.org/abs/cs/0702074): $$n\left ( 1-\pi r^{2} \right )^{n-1}$$
Instead of equal radii circles, what if the radii are polydisperse and for example follow a lognormal distribution - how might we find the expected number of isolated nodes?