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.