  We study the probability distribution function (PDF) of the mass density in
simulations of supersonic turbulence with properties appropriate for molecular
clouds. For this study we use Athena, a new higher-order Godunov code. We find
there are surprisingly similar relationships between the mean of the
time-averaged PDF and the turbulent Mach number for driven hydrodynamic and
strong-field MHD turbulence. There is, however, a large scatter about these
relations, indicating a high level of temporal and spatial variability in the
PDF. Thus, the PDF of the mass density is unlikely to be a good measure of
magnetic field strength. We also find the PDF of decaying MHD turbulence
deviates from the mean-Mach relation found in the driven case. This implies
that the instantaneous Mach number alone is not enough to determine the
statistical properties of turbulence that is out of equilibrium. The scatter
about the mean-Mach relation for driven turbulence, along with the large
departure of decaying turbulence PDFs from those of driven turbulence, may
illuminate one factor contributing to the large observed cloud-to-cloud
variation in the star formation rate per solar mass.
