Now let us draw N samples 
from the pdf 
and
define the
following linear combination of the samples:
where the parameters 
are real constants and the 
are
real-valued functions.
Since the 
are r.v.'s, and G is a linear combination of functions of the
r.v.'s, G is also a r.v. We now examine the properties of G, in particular
its expectation value and variance. Referring to our earlier discussion of the
mean and variance of a linear combination, expressed as Eq. (9) and
Eq. (15),
respectively, we find
