On triple mutual information (Q1902817)

The mutual information of two random variables plays fundamental roles in many areas of applied mathematics. This quantity can be generalized to finite sets of random variables. In contrast to the nonnegativity of the usual mutual information, the triple mutual information can be negative as well as positive and its sign gives us a rough indication of the mode of mutual dependency among three random variables. The purpose of this note is to determine the range of the triple mutual information and to examine when the extremals are attained.