I am given that (strictly greater) and
I am to deduce whether B and C could be independent.
I am thinking no.
In order for the right side to be equal to this means at least
Now, since it was given that
, since this would make
However implies and are not independent in this case because and ( since )
and not independent implies and aren't independent.
Is this sound reasoning? I am skeptical because this based of the converse of a true statement.