  In this work, we investigate the problem of finding surfaces in the
Lorentz-Minkowski 3-space with prescribed skew ($S$) and mean ($H$) curvatures,
which are defined through the discriminant of the characteristic polynomial of
the shape operator and its trace, respectively. After showing that $H$ and $S$
can be interpreted in terms of the expected value and standard deviation of the
normal curvature seen as a random variable, we address the problem of
prescribed curvatures for surfaces of revolution. For surfaces with a
non-lightlike axis and prescribed $H$, the strategy consists in rewriting the
equation for $H$, which is initially a nonlinear second order Ordinary
Differential Equation (ODE), as a linear first order ODE with coefficients in a
certain ring of hypercomplex numbers along the generating curves: complex
numbers for curves on a spacelike plane and Lorentz numbers for curves on a
timelike plane. We also solve the problem for surfaces of revolution with a
lightlike axis by using a certain ODE with real coefficients. On the other
hand, for the skew curvature problem, we rewrite the equation for $S$, which is
initially a nonlinear second order ODE, as a linear first order ODE with real
coefficients. In all the problems, we are able to find the parameterization for
the generating curves in terms of certain integrals of $H$ and $S$.
