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Memory-state [low-resistance state (RL) and high-resistance state (RH)] dependence of random telegraph noise (RTN) of Ta2O5/TiO2 resistive random access memory is investigated. The conduction mechanism of both memory states and a limit of resistance controllability are also investigated to clarify the difference in the RTN mechanism of both states. The boundary between the RL and RH states was found at 5-20 kΩ , and the conduction mechanism much depended on the memory state. The noise also depended on the memory state. The noise amplitude in the RH state was larger than that in the RL state. In the RH state, a tunnel barrier was generated to cut off a conduction path (filament), and traps inside the tunnel barrier were supposed to increase the noise amplitude. Moreover, the composition of the following degraded the noise distribution in the RH state: 1) capture and emission of charges with traps and 2) instability of these traps against the bias temperature stress.