  We studied the Active Galactic Nuclei (AGN) radio emission from a compilation
of hard X-ray selected samples, all observed in the 1.4 GHz band. A total of
more than 1600 AGN with 2-10 keV de-absorbed luminosities higher than 10^42
erg/s were used. For a sub-sample of about 50 z\lsim 0.1 AGN it was possible to
reach a ~80% fraction of radio detections and therefore, for the first time, it
was possible to almost completely measure the probability distribution function
of the ratio between the radio and the X-ray luminosity Rx=log[L(1.4)/Lx]. The
probability distribution function of Rx was functionally fitted as dependent on
the X-ray luminosity and redshift, P(Rx|Lx,z). It roughly spans over 6 decades
(-7<Rx<-1), and does not show any sign of bi-modality. It resulted that the
probability of finding large values of the Rx ratio increases with decreasing
X-ray luminosities and (possibly) with increasing redshift. No statistical
significant difference was found between the radio properties of the X-ray
absorbed and unabsorbed AGN. The measure of the probability distribution
function of Rx allowed us to compute the kinetic luminosity function and the
kinetic energy density which, at variance with what assumed in many galaxy
evolution models, is observed to decrease of about a factor of five at redshift
below 0.5. About half of the kinetic energy density results to be produced by
the more radio quiet (Rx<-4) AGN. In agreement with previous estimates, the AGN
efficiency in converting the accreted mass energy into kinetic power is, on
average, ~5x10-3.
