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When k(x,Y) "<.is~a quasi-monotone function a.'1d the random variables X and Y have fixed distributions, it is sho1~ under some further mild conditions that Ek(X,Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions.
ABSTUCT The problem of optimally allocating partially effective, defensive weapons against randomly arriving enemy aircraft so that a bomber maximizes its probability of reaching its designated target is considered in the usual continuous-time context, and in a discrete-time context. The problem becomes that of determining the optimal number of missiles(More)
For an arbitrary point of a homogeneous Poisson point process in a d-dimen-siona! Euclidean space, consider the number of Poisson points that have that given point as their r-th nearest neighbor (r = 1,2,...). It is shown that as d tends to infinity, these nearest neighbor counts (r = 1,2,...) are tid asymptotically Poisson with mean 1. The proof relies on(More)