The mode locking of a Raman fiber laser with an amplified spontaneous emission (ASE) pump source is investigated for performance improvement. Raman dissipative solitons with a compressed pulse duration of 1.05 ps at a repetition rate of 2.47 MHz are generated by utilizing nonlinear polarization rotation and all-fiber Lyot filter. A signal-to-noise ratio as high as 85 dB is measured in a radio-frequency spectrum, which suggests excellent temporal stability. Multiple-pulse operation with unique random static distribution is observed for the first time, to the best of our knowledge, at higher pump power in mode-locked Raman fiber lasers.