Now consider the special case where 
and 
:
Note that G is simply the average value of the N sampled r.v.'s. Now consider the expectation value for G, using Eq. (61):
In other words, the expectation value for the average ( not
the average itself!)
of N observations of the r.v. 
is simply the expectation value for
.
This statement is not as trivial as it may seem, because we may not know
in
general, because 
is a property of 
and the pdf 
.
However,
Eq. (62) assures us that an average of N observations of 
will be a
reasonable estimate of 
.
Later, we will introduce the concept of an unbiased estimator, and suffice to
say for now, that Eq. (62) proves that the simple average is an unbiased
estimator for the mean.
Now let us consider the variance in G, in particular its dependence on the
sample size.
