Please /please/ don’t use the “+” sign like that! H(X+Y+Z) should be H(X,Y,Z).
“So for the joint distribution X+Y there are” should be “So for the joint distribution of X and Y there are”
etc.
I was skimming your post, misunderstood your meaning entirely and started wondering if you had made a mistake until I went back and noticed that some of your “+”s meant “X and Y” rather than “the value of X plus the value of Y”.
(So for example, when I read “”“ Z has two states, “even” and “odd”, perfectly correlated to the evenness or oddness of X+Y. In fact, we’ll suppose that Z is just the question “Are X+Y even or odd?” “”” I thought “golly, ‘Are’ X+Y even or odd? Must be a grammar mistake.”)
Now granted, it was easy to tell what you really meant after I slowly read through the introductory paragraph, but please change it, because:
It will confuse mathematicians who are skimming because they’ve seen things like this before
You use the other sense of “+” in your equations, and there’s no excuse for operator overloading if it can be avoided.
The books I’ve read just say “XY” or “X,Y” if they need a name for the joint variable.
It’s not just non-standard, but used inconsistantly. You say H(X+Y+Z) in one place and H(X,Y) in another.
Nice post. However:
Please /please/ don’t use the “+” sign like that! H(X+Y+Z) should be H(X,Y,Z). “So for the joint distribution X+Y there are” should be “So for the joint distribution of X and Y there are” etc. I was skimming your post, misunderstood your meaning entirely and started wondering if you had made a mistake until I went back and noticed that some of your “+”s meant “X and Y” rather than “the value of X plus the value of Y”. (So for example, when I read “”“ Z has two states, “even” and “odd”, perfectly correlated to the evenness or oddness of X+Y. In fact, we’ll suppose that Z is just the question “Are X+Y even or odd?” “”” I thought “golly, ‘Are’ X+Y even or odd? Must be a grammar mistake.”) Now granted, it was easy to tell what you really meant after I slowly read through the introductory paragraph, but please change it, because:
It will confuse mathematicians who are skimming because they’ve seen things like this before
You use the other sense of “+” in your equations, and there’s no excuse for operator overloading if it can be avoided.
The books I’ve read just say “XY” or “X,Y” if they need a name for the joint variable.
It’s not just non-standard, but used inconsistantly. You say H(X+Y+Z) in one place and H(X,Y) in another.