Mutual Information Notation

Question

I am confused about the difference which the use of ";" and "," causes in the following expressions for defining mutual information between X and Y

$ I(X ; Y) $ and $ I(X , Y) $

Answer 1

I believe it is because $I(X;Y) = I(Y;X)$. Mutual information does not measure a directional information flow, but how much $X$ can tell you about $Y$, and vice versa.

In addition, sometimes it is necessary to represent MI between $(X,Y)$ and $Z$, in which case $I(X,Y;Z)$ would be a sufficient notation.