For an equation Z = f(X,Y) between random variables the problem of the determination or estimation of the e.p.d P^X/Z is considered under a fixed marginal distribution P^Y and a certain assumption on the joint of p.d. of the variables. This assumption may be interpreted in the sense, that the realization of Z contains no the realization Y with exception of its range. Lower and upper bounds are given for th c.p.d., which are identical, if the equation may be solved for X. The result is illustrated by the example of a linear filter. Furthermore it is shown, that the theory of structural statistical inference of Fraser may be developed in the frame of probability theory without transformation groups, revealing the essential assumption exploited in this theory.