  The Random Variable Transformation (RVT) method is a fundamental tool for
determining the probability distribution function associated with a Random
Variable (RV) Y=g(X), where X is a RV and g is a suitable transformation. In
the usual applications of this method, one has to evaluate the derivative of
the inverse of g. This can be a straightforward procedure when g is invertible,
while difficulties may arise when g is non-invertible. The RVT method has
received a great deal of attention in the recent years, because of its crucial
relevance in many applications. In the present work we introduce a new approach
which allows to determine the probability density function of the RV Y=g(X),
when g is non-invertible due to its non-bijective nature. The main interest of
our approach is that it can be easily implemented, from the numerical point of
view, but mostly because of its low computational cost, which makes it very
competitive. As a proof of concept, we apply our method to some numerical
examples related to random differential equations, as well as discrete
mappings, all of them of interest in the domain of applied Physics.
