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Several investigations of the X-ray variability of active galactic nuclei(AGN) using the normalised excess variance (${\sigma^2_{\rm NXS}}$) parameterhave shown that variability has a strong anti-correlation with black hole mass($M_{\rm BH}$) and X-ray luminosity ($L_{\rm X}$). In this study we confirmthese previous correlations and find no evidence of a redshift evolution. Usingobservations from XMM-Newton, we determine the ${\sigma^2_{\rm NXS}}$ and$L_{\rm X}$ for a sample of 1091 AGN drawn from the XMM-Newton Cluster Survey(XCS) - making this the largest study of X-ray spectral properties of AGNs. Wecreated light-curves in three time-scales; 10 ks, 20 ks and 40 ks and usedthese to derive scaling relations between ${\sigma^2_{\rm NXS}}$, $L_{\rm X}$(2.0-10 keV range) and literature estimates of $M_{\rm BH}$ from reverberationmapping. We confirm the anti-correlation between $M_{\rm BH}$ and${\sigma^2_{\rm NXS}}$ and find a positive correlation between $M_{\rm BH}$ and$L_{\rm X}$. The use of ${\sigma^2_{\rm NXS}}$ is practical only for pointedobservations where the observation time is tens of kiloseconds. For muchshorter observations one cannot accurately quantify variability to estimate$M_{\rm BH}$. Here we describe a method to derive $L_{\rm X}$ from shortduration observations and used these results as an estimate for $M_{\rm BH}$.We find that it is possible to estimate $L_{\rm X}$ from observations of just afew hundred seconds and that when correlated with $M_{\rm BH}$, the relation isstatistically similar to the relation of $M_{\rm BH}$-$L_{\rm X}$ derived froma spectroscopic analysis of full XMM observations. This method may beparticularly useful to the eROSITA mission, an all-sky survey, which willdetect $>$10$^{6}$ AGN.

Correlations between X-ray properties and Black Hole Mass in AGN:  towards a new method to estimate black hole mass from short exposure X-ray  observations