We report here a novel architecture for a random fiber laser exploiting the combination of a semiconductor optical amplifier (SOA) and an erbium doped fiber (EDF). The EDF was optically biased by a continuous wave pump laser, whereas the SOA was arranged in a fiber loop-mirror and driven by nanosecond duration current pulses. Laser pulses were obtained by synchronizing the SOA driver to the returning amplified Rayleigh back-scattered light from a selected short section of the EDF. By tuning the SOA pulse rate, random lasing was achieved by addressing selected meter-long sections of the 81-m long EDF, which was open-ended. Laser oscillation can be potentially obtained with SOA modulation frequencies from several kHz to the MHz regime. We discuss the mechanism leading to the hybrid random laser emission, connecting with phase sensitive optical time domain reflectometry and envision potential applications of this electronically addressable random laser.