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