A sufficient condition for conditional expectation to be monotonically related to distribution parameters

In this paper we give a sufficient condition for conditional expectation to be a monotonic function of a parameter of the joint probability distribution. A second sufficient condition is given for the case where varying the parameter of the joint distribution leaves the shape of that distribution unchanged. Finally, an application of the condition is illustrated on the counter models for choice reaction time of LaBerge (1962) and Nickerson (1969).