  We present a statistical study of several fundamental properties of radio
sources in nearby clusters, including the radial distribution within clusters,
the radio luminosity function (RLF), and the fraction of galaxies that is
radio-active (radio active fraction, RAF). The analysis is carried out for a
sample of 573 clusters detected in the X-ray and also observed at 1.4 GHz in
the NVSS. K-band data from the 2MASS are used to identify the brightest cluster
galaxies (BCGs), and to construct the K-band LF. Our main results include: (1)
The surface density profile of radio-loud AGNs is much more concentrated than
that of all galaxies, and can be described by the NFW profile with
concentration ~ 25. (2) A comparison of the RLFs in the clusters and in the
field shows that the cluster AGN number density is about 5,700 times higher,
corresponding to a factor of 6.8 higher probability of a galaxy being radio
active in the cluster than in the field. We suggest that about 40-50% of
radio-loud AGNs in clusters may reside in low mass galaxies (M_K>-23). (3) The
RAFs of cluster galaxies of different stellar mass are estimated. About 5% of
galaxies more luminous than the characteristic luminosity (M_K<M_*~-24) host
radio-loud AGNs. The RAF for BCGs is >30%, and depends on the cluster mass.
Compare to the field population, cluster galaxies have 5-10 times higher RAF.
Combining the AGN RLF and spatial distribution within clusters, we estimate
that they may inject an energy of ~0.13 keV per particle to the intracluster
medium near the cluster center. We also investigate the degree of contamination
by cluster radio sources on the yields of SZE cluster surveys, and estimate
that as many as 10% of clusters detected at 150 GHz may host AGNs whose flux is
comparable to the cluster SZE signal. (abridged)
