  The relation between X-ray and UV/optical variability in AGNs has been
explored in many individual sources, however a large sample study is yet
absent. Through matching the XMM-Newton serendipitous X-ray and UV source
catalogs with SDSS quasars, we build a sample of 802 epoch-pairs of 525 quasars
showing clear variability in logFx-logFuv space. After correcting for the
effect of photometric noise, we find 35.6\pm2.1% of the epoch-pairs show
asynchronous variability between X-ray and UV (brightening in one band but
dimming in the other). This indicates only in 28.8\pm4.2% of the epoch-pairs
the X-ray and UV variability are intrinsically coordinated. The variability
synchronicity exhibits no dependence on physical parameters of quasars or the
time lag of the epoch-pairs, except for stronger variability tends to have
stronger synchronicity. Switches between synchronous and asynchronous
variability are also seen in individual sources. The poor coordination clearly
contradicts both the X-ray reprocessing model and the accretion rate variation
model for AGN variability. The ratios of the observed X-ray variability
amplitude to that in UV span a broad range and peak at ~ 2. The dominant
fraction of the ratios appear too small to be attributed to X-ray reprocessing,
and too large for accretion rate variation. The inhomogeneous disk model which
incorporates both X-ray and UV/optical variability in AGNs is favored by the
observed stochastic relation between X-ray and UV variations.
