Formulas for interpolating between probability density and mass functions in spaces of arbitrary dimensionality are presented. These formulas are intended to be an alternative to repeating costly Monte Carlo simulations of systems with random uncertainty when some of the deterministic parameters are changed. It is found that the given formulas produce accurate results even with relatively coarse meshes. As the mesh is refined, the accuracy of the interpolated quantities increases; accordingly, in addition to the more complicated and robust interpolation formulas meant for the case of a coarse mesh, simplified versions that result in good accuracy with a fine mesh are also presented. Savings in computational effort up to a factor of one hundred are common even with the more complicated formulas, indicating that interpolation is a lucrative alternative to Monte Carlo simulation when the complete probability distribution, as opposed to only the low-order statistics, is needed.