A Statistical Coverage Problem

This paper discusses the total expected coverage of a target subjected to several shots, each of which has circularly symmetric aiming errors. Both point and diffuse targets are considered and the various aiming points are arbitrary with respect to the target center. For the particular case in which the expected coverage is proportional to the exponent of the square of the distance between the impact point and the target, closed-form expressions are derived. The results have application to the evaluation of various weapon systems, targeting strategy, and two-dimensional search theory.