The cancellation of the last term in Eq. (15) for independent r.v.'s motivates the concept of the covariance.
If x and y are independent, then 
.
However, it is possible to have
even if x and y are not independent.
It should be noted that the
covariance can be negative. A related quantity that arises often in
statistical analysis is the correlation coefficient,
which is a convenient measure of the degree
to which two r.v.'s are correlated (or anti-correlated).
It is easily shown that 
.
