  The goal of this paper is to study convergence and error estimates of the
Monte Carlo method for the Navier-Stokes equations with random data. To
discretize in space and time, the Monte Carlo method is combined with a
suitable deterministic discretization scheme, such as a finite volume method.
We assume that the initial data, force and the viscosity coefficients are
random variables and study both, the statistical convergence rates as well as
the approximation errors. Since the compressible Navier-Stokes equations are
not known to be uniquely solvable in the class of global weak solutions, we
cannot apply pathwise arguments to analyze the random Navier-Stokes equations.
Instead we have to apply intrinsic stochastic compactness arguments via the
Skorokhod representation theorem and the Gy\"{o}ngy-Krylov method. Assuming
that the numerical solutions are bounded in probability, we prove that the
Monte Carlo finite volume method converges to a statistical strong solution.
The convergence rates are discussed as well. Numerical experiments illustrate
theoretical results.
