On some bivariate discrete distributions with multivariate components

Consider a random vector (X,Y) where X=(X1,X2, ...., Xs,) and Y=(Y1,Y2, Ys) with Xi, Yi, i=1,2,..., s independent non-negative, integer-valued variables finite support such that X>=Y. We show in the case distribution of (YlX=n) is certain structural form then there exists relationship between distributions Y Y|(X=Y) which uniquely determines X. The question less stringent condition independence X-Y usually involved pro¬blems this nature. Examples are given to illustrate result. X,Y have infinite has been examined earlier by author.