For independent random variables X and Y, define S --- X + Y.
When the conditional expectations E[g(X) I S] - a(S) and E[h(X) I S] - b(S)
are given, then under certain assumptions, the density function of X has the
form of u(x)k(a)e ~, where u(x) is uniquely determined by the functions a(.)
and b(.).
Relation:
Far east journal of mathematical sciences 1, pp.837-847
