Easily Stated but Hard Statistical Problems

This is an expository paper written in response to an invitation to give a non-technical talk in a session devoted to Practical Aspects of Statistics at the 1986 Annual Statistical Meetings. The goal of the session is to encourage interest in statistics among non-statisticians. The author chose to describe three problems of current research interest. The problems have the feature that they can be stated in a relatively easy fashion. The solutions however are difficult. References to partial solutions are given all three problems have aspects that remain unsolved and are currently under study. The problem of Section 2 deals with survivorship data and concerns estimation of average remaining life. Section 3 considers a problem that pertains to assessing the degree of similarity between species presence or absence on islands. Section 4 presents a problem in geometrical probability. To conform to the spirit of the session, I have chosen to describe the problems in words, de- emphasizing symbols and mathematics and aiming for the non-statistician.