On the Degree of Mutual Dependence of Three Events.

We define degree of mutual dependence of three events in a probability space by using Boltzmann-Shannon entropy function of an appropriate variable distribution produced by these events and depending on four parameters varying, in general, within of a polytope. It turns out that the entropy function attains its absolute maximum exactly when the three events are mutually independent and its absolute minimum at some vertices of the polytope where the events are "maximally" dependent. By composing the entropy function with an appropriate linear function we obtain a continuous "degree of mutual dependence" function with the same domain and the interval [0, 1] as a target. It attains value 0 when the events are mutually independent (the entropy is maximal) and value 1 when they are "maximally" dependent (the entropy is minimal). A link is available for downloading a Java code which evaluates the degree of mutual dependence of three events in the classical case of a sample space with equally likely outcomes. [ABSTRACT FROM AUTHOR]