Large, rapidly growing literature is available on bipolar resistive-switching random access memories (RRAM) made of myriad of simple and advanced materials. Many of them exhibit similar resistance switching behavior but, until now, no unifying model can allow quantification of their voltage and time responses. Using a simple parallel circuit model, these responses of a newly discovered RRAM made of a thin-film random material are successfully analyzed. The analysis clearly reveals a large population of intermediate states with remarkably similar switching characteristics. Such modeling framework based on simple circuit constructs also appears applicable to several RRAM made of other materials. This simple approach to analyze data write/rewrite and memory retention in RRAM may aid their further understanding and development.