Generalized optimal search paths for continuous univariate random variables

The purpose of this paper is to solve the Generalized Linear Search Problem for continuous random variables. This problem is concerned with finding a target located on a line. The position of the target is given by the value of a random variable which has a prior distribution. A searcher starts looking for the target from some point, moving along with an upper bound on his speed. The target being sought for might be in either direction from the starting point, so the searcher needs to change his direction many times before he attains his goal. With minimality of average time to target detection as the measure of optimality of search paths, the paper has obtained algorithms that find such paths for those targets which have absolutely continuous distributions. More detailed properties of optimal search paths are, also studied. One of the main results is that: these search paths are not minimal, in some cases, for some types of target distributions.