In order to illustrate some of the basic principles of statistical mechanics, a study is made of the nonequilibrium behavior of a one-dimensional particle confined to a finite box with perfectly reflecting walls. The statistical aspects of the analysis are due to the incompleteness of the initial information. Liouville's equation is solved exactly and completely, and it is shown that this finite, isolated, reversible system exhibits irreversible statistical behavior. By applying information theory to the results obtained, it is shown that the irreversibility exhibited by this system consists in the information becoming less relevant to the experiments which can be performed on the system.