  Recent X-ray variability studies suggest that the log of the square of the
fractional rms variability amplitude, rms^2, seems to correlate with the log of
the AGN black-hole mass, M_BH, with larger black holes being less variable for
a fixed time interval. This has motivated the theoretical modeling of the
rms^2-M_BH correlation with the aim of constraining AGN masses based on X-ray
variability. A viable approach to addressing this problem is to assume an
underlying power spectral density with a suitable mass dependence, derive the
functional form of the rms^2-M_BH correlation for a given sampling pattern, and
investigate whether the result is consistent with the observations. For
simplicity, previous studies, inspired by the similarities shared by the timing
properties of AGN and X-ray binaries, have explored model power spectral
densities characterized by broken power laws. and ignored, in general, the
distorting effects that the particular sampling pattern imprints in the
observed power spectral density. Motivated by the latest timing results from
X-ray binaries, obtained with RXTE, we propose that AGN broad-band noise
spectra consist of a small number of Lorentzian components. This assumption
allows, for the first time, to fully account for sampling effects in
theoretical models of X-ray variability in an analytic manner. We show that,
neglecting sampling effects when deriving the fractional rms from the model
power spectral density can lead to underestimating it by a factor of up to 80%
with respect to its true value for the typical sampling patterns used to
monitor AGN. We discuss the implications of our results for the derivation of
AGN masses using theoretical models of the rms^2-M_BH correlation. (Abridged)
