We present a systematic X-ray study of eight AGNs with intermediate mass black holes (M_BH 8-95x10^4 Msun) based on 12 XMM-Newton observations. The sample includes the two prototype AGNs in this class - NGC4395 and POX52 and six other AGNs discovered with the SDSS. These AGNs show some of the strongest X-ray variability with the normalized excess variances being the largest and the power density break time scales being the shortest observed among radio-quiet AGNs. The excess variance -- luminosity correlation appears to depend on both the BH mass and the Eddington luminosity ratio. The break time scale -- black hole mass relations for AGN with IMBHs are consistent with that observed for massive AGNs. We find that the FWHM of the Hbeta or Halpha line is uncorrelated with the BH mass, but shows strong anticorrelation with the Eddington luminosity ratio. Four AGNs show clear evidence for soft X-ray excess emission (kT_in~150-200eV). X-ray spectra of three other AGNs are consistent with the presence of the soft excess emission. NGC4395 with lowest L/L_Edd lacks the soft excess emission. Evidently small black mass is not the primary driver of strong soft X-ray excess emission from AGNs. The X-ray spectral properties and optical-to-X-ray spectral energy distributions of these AGNs are similar to those of Seyfert 1 galaxies. The observed X-ray/UV properties of AGNs with IMBHs are consistent with these AGNs being low mass extension of more massive AGNs; those with high Eddington luminosity ratio looking more like narrow-line Seyfert 1s while those with low $L/L_{Edd}$ looking more like broad-line Seyfert 1s.
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