  There is increasing evidence that AGN mechanical feedback is important in the
energetics of cooling flows in galaxies and galaxy clusters. We investigate the
implications of the variability of AGN mechanical luminosity L_m on
observations of cooling flows and radio galaxies in general. It is natural to
assume that l=ln(L_m/L_x) is a Gaussian process. Then L_m will be log-normally
distributed at fixed cooling luminosity L_x, and the variance in a measure of
L_m will increase with the time-resolution of the measure. We test the
consistency of these predictions with existing data. These tests hinge on the
power spectrum of l(t). Monitoring of Seyfert galaxies combined with estimates
of the duty cycle of quasars imply flicker noise spectra, similar to those of
microquasars. We combine a sample of sources in cooling flows that have
cavities with the assumption that the average mechanical luminosity of the AGN
equals L_x. Given that the mechanical luminosities are characterized by flicker
noise, we find that their spectral amplitudes lie between the estimated
amplitudes of quasars and the measured values for the radio luminosities of
microquasars. The model together with the observation that powerful radio
galaxies lie within a narrow range in optical luminosity, predicts the
luminosity function of radio galaxies, in agreement with observations.
Forthcoming radio surveys will test the prediction that the luminosity function
turns over at about the smallest luminosities so far probed. [Abridged]
