We report random noise pulsed regime of an ytterbium-doped fiber laser arranged in common Fabry-Perot configuration. We show that the laser output obeys the photon statistics inherent to narrowband amplified spontaneous emission and that the noise pulsing is properly addressed in terms of probability density and autocorrelation functions. Our novel approach reveals, in particular, that the regime's coherence time dramatically shortens, from few ns to tens ps, with increasing laser power.