Conditional independence and predictive copula

In this paper, we address the concept of conditional independence between two random variables X and Y given the entity Θ. We identify the impact of conditional independence on the analytic form of the predictive 2-copula between X and Y. We obtain a representation of the predictive 2-copula between X and Y in terms of functions associated with the copulas between X and Θ and between Y and Θ. Through the concept of infinite exchangeable sequences we amplify the validity of our results, obtaining the predictive 2-copula between two variables in terms of the copula between only one of these variables and the quantity Θ.