**Beware:**

If we need to take a function of a random variable,
we cannot in general say that the expectation of the function is
the function of the expectation, look for instance at
the function *g*(*X*)=*X*^{2}, for the random variable
*X* which takes on -1 with probability 1/5,
+1 with probability .3,
and 0 with probability 1/2.

For this random variable
*E*[*X*]=.1 and *E*[*X*^{2}]=.5 which is NOT the same as
.01=(*E*[*X*])^{2}.

For any two random variables *X* and *Y*,
we have:

Only for independent random variables do we have