  (abridged) We present the results of a variable star search in Andromeda II,
a dwarf spheroidal galaxy companion to M31, using HST/WFPC2 observations.
Seventy-three variables were found, one of which is an anomalous Cepheid while
the others are RR Lyrae stars. The anomalous Cepheid has properties consistent
with those found in other dwarf spheroidal galaxies. For the RR Lyrae stars,
the mean periods are 0.571 day and 0.363 day for the fundamental mode and
first-overtone mode stars, respectively. With this fundamental mode mean period
and the mean metallicity determined from the red giant branch (<[Fe/H]>=-1.49),
Andromeda II follows the period-metallicity relation defined by the Galactic
globular clusters and other dwarf spheroidal galaxies. We also find that the
properties of the RR Lyrae stars themselves indicate a mean abundance that is
consistent with that determined from the red giants. There is, however, a
significant spread among the RR Lyrae stars in the period-amplitude diagram,
which is possibly related to the metallicity spread in Andromeda II indicated
by the width of the red giant branch in Da Costa et al. In addition, the
abundance distribution of the RR Lyrae stars is notably wider than the
distribution expected from the abundance determination errors alone. The mean
magnitude of the RR Lyrae stars, <V_RR>=24.87+/-0.03, implies a distance
d=665+/-20 kpc to Andromeda II. We also demonstrate that the specific frequency
of anomalous Cepheids in dwarf spheroidal galaxies correlates with the mean
metallicity of their parent galaxy, and that the Andromeda II and Andromeda VI
anomalous Cepheids appear to follow the same relation as those in the Galactic
dwarf spheroidals.
