I am trying to figure the following out:
Let Z,X be random variables and Y = X + Z;
For a known f(X) and g(Z), and a given data set of Y it is required to find the parameters of f and g functions.
I wonder if this is at all possible. If f and g are Normal then the distribution of Y is also Normal with the sum of means and variances of f and g. In this case I presume it is not possible to derive the mean of X and Z separately. Is this true? and if it is is this true for any arbitrary pair of functions f and g.