Formulations are presented for the first and second moments of the storage state distribution in terms of the moments of the inflow distribution. These expressions give explicit consideration to the maximum and minimum storage bounds in the reservoir system, a feature which is not incorporated in some existing formulations based on traditional control theory. Using these formulations, solutions are derived for the mean and variance of the storage state variables for specified drafts, using a non-linear solver. The approach presented does not involve any discretization of the system variables. Estimates are obtained for the probability of spills and deficits (or alternately reliability). These estimates are used for approximating the storage state distribution using a double bounded density function. The results of an annual reliability study and estimates of the storage state distribution for a single reservoir system, based on the formulations proposed, are presented and compare favourably with corresponding results derived from simulation.