  Although flux variability is one of the defining properties of accretion
flows onto supermassive black holes, its dependence on physical parameters such
as the mass of the compact object and the Eddington ratio remain under
discussion. In this paper we address this issue using the structure function
statistic to measure the variability at X-ray wavelengths of a sample of
optically selected QSOs with available black hole masses and Eddington ratios.
We present a new Bayesian methodology for estimating the structure function
tailored to the Poisson nature of the X-ray data. This is applied to 15,548
SDSS DRQ16 QSOs with repeat observations in the XMM-Newton archive and/or the
SRG/eROSITA All Sky Survey. The X-ray structure function monotonically
increases to time intervals of about 10-15 years, suggesting a preference for
scenarios in which instabilities of the accretion disk contribute to the X-ray
variability on long timescales. Additionally, there is evidence that the
amplitude of the stochastic X-ray flux variations rises with decreasing black
hole mass and Eddington ratio. This finding imposes stringent constraints on
empirical models of Active Galactic Nuclei variability derived from local
samples, emphasizing the significance of high-redshift population studies for
comprehending the stochastic flux variations in active black holes.
