2. [30 points]
Suppose 
, 
, 
are i.i.d. random
variables with the exponential distribution having
mean 
. That is, the density is given by
Let
denote the sample mean. Of course, the ``population'' variance is
Show that for some 
,
and determine the value of .
Solution:
We will apply the 
-method:
If 
where 
and if h is a function
differentiable at , then
.
Of course,
So, applying the -method with
, we have 
= 
and
i.e., in (15) is
. (NOTE: We know that it
would have to be a 4'th power of
just by dimensional analysis.)
