Generalized Hit Probabilities with a Gaussian Target, II

In a recent paper [2] the author developed a discrete distribution and several derived limiting distributions for the number of "hits" on a k-dimensional Gaussian target. The purpose of the present paper is to apply these results to the two-dimensional problem considered by Cunningham and Hynd [1]. A general expression and two limiting forms are obtained for the probability of at least one hit. The numerical evaluation using the data in [1] is considered for $n = 5$ rounds, and the probability of at least one hit is plotted in Fig. 1 for various combinations of aiming and dispersion error. For a given over-all time interval the evaluation for large n is discussed in Section 5 and illustrated using the data from [1].