  We present a study of the Gaussian q-measure introduced by Diaz and Teruel
from a probabilistic and from a combinatorial viewpoint. A main motivation for
the introduction of the Gaussian q-measure is that its moments are exactly the
q-analogues of the double factorial numbers. We show that the Gaussian
q-measure interpolates between the uniform measure on the interval [-1,1] and
the Gaussian measure on the real line.
