  We investigate statistical properties of LRGs in a sample of X-ray selected
galaxy clusters at intermediate redshift ($0.2\le z\le0.6$). The LRGs are
selected based on carefully designed color criteria, and the cluster membership
is assessed via photometric redshifts. As clusters and LRGs are both viewed as
promising tracer of the underlying dark matter distribution, understanding the
distribution of LRGs within clusters is an important issue.
  Our main findings include:
  1. The halo occupation distribution of LRGs inside our cluster sample is
$N(M) = k\times (M/10^{14})^{a}$ where $a=0.620\pm 0.105 $ and $k=1.425\pm0.285
$ assuming a Poisson distribution for $N(M)$.
  2. The halo occupation distribution of LRGs ($N(M)$) and the satellite
distribution of LRGs ($N-1(M)$) are both consistent with being Poisson. To be
more quantitative, we find $Var(N)/<N>= 1.428\pm 0.351$ and $Var(N-1)/<N-1> =
1.823 \pm 0.496$
  3. The radial profile of LRGs within clusters when fitted with a NFW profile
gives a concentration of $17.5^{+7.1}_{-4.3}$ ($6.0^{+3.2}_{-1.9}$) including
(excluding) BLRGs (Brightest LRGs).
  We also discuss the implications of these observations on the evolution of
massive galaxies in clusters.
