the program SHOULD live in your applications folder. just saying...
as for "a copy of the program as a back up"
you kind of can't - there's enough bits n pieces of it in various places to make that pretty hard.
i mean you could TRY just copying the app/s across to another system and see what happens.
there's a few other things to copy that might make it work
from your main system drive > Library > Application Support there are three Final Cut folders, and also the ProApps folder,
and possibly the Soundtrack Pro folder
they'd have to go in the same spot on the other system.
likewise Homefolder > Library > Application Support > Final Cut Studio (this is just for the other apps)
also in Homefolder >Library > Preferences are lots of bits n pieces, but I'm pretty sure that they will get created when you launch the app.
best thing to do as some sort of safety back-up is to make a clone of your entire system.
i use Carbon Copy Cloner for that. friends use SuperDuper
maybe before you do that, create a new user.
then if possible, clone just that user, not all your own mail, and pictures etc etc.
if you can't selectively clone a user, clone all and secure erase your user folder when it's done
then you'd have a pretty clean backup system.
check to see if it works of course !
hope that helps,
nick