The Nearest Star
Points are scattered over the plane according to a homogeneous Poisson process with an average of 1 point per unit area. What is the expected distance from the origin to the nearest point? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Gap Between Two Lifetimes 4.0/10
- Two Buses in a Row 3.0/10
- The Quiet Line 3.0/10
Source: Classic nearest-neighbour calculation for a planar Poisson process, in wide circulation; no traceable original source. Statement written for AxiomIQ.