In this paper, we consider the effect of stochastic pumps on the parametric instabilities, including the pump band-width effect, the effect of the frequency mismatch and of the plasma temperature fluctuations that are induced by the fluctuations in the pump itself. Contrary to what is found in the literature, the threshold for instability can initially decrease with increasing pump band-width and reach a minimum when these effects are included. We propose a physical explanation of this minimum and point out the relationship between the thresholds for the instability of the mean energy and mean amplitude of the wave. The pump amplitude and the resulting plasma temperature fluctuations compete with the pump band-width and decrease the threshold for instability. Even for large pump band-widths, the threshold for instability for a pump with fluctuating amplitude is always lower than for the coherent one. Our general conclusion is that, in studying the effect of stochastic pumps on parametric instabilities more realistically, one has to include, in addition to the pump band-width, a number of other phenomena like imperfect frequency matching, the fluctuations induced in plasma parameters and the amplitude fluctuations of the pump itself.