  We analyse the distribution of CO brightness temperature and integrated
intensity in M51 at ~40 pc resolution using new CO data from the Plateau de
Bure Arcsecond Whirlpool Survey (PAWS). We present probability distribution
functions (PDFs) of the CO emission within the PAWS field, which covers the
inner 11 x 7 kpc of M51. We find variations in the shape of CO PDFs within
different M51 environments, and between M51 and M33 and the Large Magellanic
Cloud (LMC). Globally, the PDFs for the inner disk of M51 can be represented by
narrow lognormal functions that cover 1 to 2 orders of magnitude in CO
brightness and integrated intensity. The PDFs for M33 and the LMC are narrower
and peak at lower CO intensities. However, the CO PDFs for different dynamical
environments within the PAWS field depart from the shape of the global
distribution. The PDFs for the interarm region are approximately lognormal, but
in the spiral arms and central region of M51, they exhibit diverse shapes with
a significant excess of bright CO emission. The observed environmental
dependence of the shape of the CO PDFs is qualitatively consistent with changes
that would be expected if molecular gas in the spiral arms has a larger range
of average densities, gas temperatures and velocity fluctuations, though
further work is required to disentangle the importance of large-scale dynamical
effects versus star formation feedback in regulating these properties. We show
that the shape of the CO PDFs for different M51 environments is only weakly
related to global properties of the CO emission, but is strongly correlated
with some properties of the local giant molecular cloud (GMC) and young stellar
cluster populations. For galaxies with strong spiral structure such as M51, our
results indicate that galactic-scale dynamical processes play a significant
role in the formation and evolution of GMCs and stellar clusters.(abridged)
