Partial Independence and Finite Distributions

Ιt is known that mere knowledge of the conditional distribution of two random variables is not sufficient to specify uniquely the marginal distributions. Some additional information is necessary. This is usually provided in some form of independence between functions of the two random variables involved. PANARETOS (1981) introduced a method of deriving the marginal distributions based on knowledge of the conditional distribution and an assumption of partial independence. An extension of this result is presented referring to truncated distributions. An interesting property of the hypergeometric distribution is revealed based on the unique decomposition of the binomial law