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Aims. Both the black hole mass and the X-ray luminosity of AGNs have beenfound to be anti-correlated with the normalized excess variance ($\sigma_{\rmrms}^2 $) of the X-ray light curves. We investigate which correlation with$\sigma_{\rm rms}^2 $ is the intrinsic one.  Methods. We divide a full sample of 33 AGNs (O' Neill et al. 2005) into twosub-samples. The black hole masses of 17 objects in sub-sample 1 weredetermined by the reverberation mapping or the stellar velocity dispersion. Theblack hole masses of the remaining 16 objects were estimated from therelationship between broad line region radius and optical luminosity(sub-sample 2). Then partial correlation analysis, ordinary least squaresregression and K-S tests are performed on the full sample and the sub-samples,respectively.  Results. We find that $\sigma_{\rm rms}^2 $ seems to be intrinsicallycorrelated with the black hole mass in the full sample. However, this seems tobe caused by including the sub-sample 2 into the analysis, which introduces anextra correlation between the black hole mass and the luminosity andstrengthens any correlation with the black hole mass artificially. Therefore,the results from the full sample may be misleading. The results from thesub-sample 1 show that the correlation between $\sigma_{\rm rms}^2 $ and theX-ray luminosity may be the intrinsic one and therefore the anti-correlationbetween $\sigma_{\rm rms}^2 $ and the black hole mass is doubtful.

Is the anti-correlation between the X-ray variability amplitude and black hole mass of AGNs intrinsic?