joint entropy

joint entropy (countable and uncountable, plural joint entropies)

1. (information theory) The Shannon entropy of a "script" whose "characters" are elements of the Cartesian product of the sets of characters of the component scripts.

   If random variables ${\displaystyle X}$ and ${\displaystyle Y}$ are mutually independent, then their joint entropy ${\displaystyle H(X,Y)}$ is just the sum ${\displaystyle H(X)+H(Y)}$ of its component entropies. If they are not mutually independent, then their joint entropy will be ${\displaystyle H(X)+H(Y)-I(X;Y)}$ where ${\displaystyle I(X;Y)}$ is the mutual information of ${\displaystyle X}$ and ${\displaystyle Y}$ .

• joint probability