The document describes PROSPECT, a tool for automatically generating synthetic data from probabilistic specifications. PROSPECT allows users to specify discrete temporal distributions declaratively and solves the specifications algebraically to obtain unique parameter solutions. If a unique distribution is defined, PROSPECT can sample from it. The document outlines PROSPECT's specification language and approach, which involves parameterizing specifications, solving systems of equations, and sampling solutions. An evaluation found PROSPECT specifications were more succinct than probabilistic programs and generated accurate data.