On The Principle of Minimum interdependence

Applying the Principle of Minimum Interdependence (abbreviated as PIM) we determine the largest product probability distribution compatible with some data on the interdependence between two or several random variables (some mixed moments of random variables). The general solution both in the discrete case and in the continuous one is given. A special analysis is done for the normal random variables. Particularly, the minimum interdependence between normal random variables compatible with the given covariance matrix is computed.