Suppose that
x_(1),x_(2),dots,x_(n)
are i.i.d.
N(\mu ,\sigma ^(2))
. a. If
\mu
is known, what is the mle of
\sigma
? b. If
\sigma
is known, what is the mle of
\mu
? c. In the case above (
\sigma
known), does any other unbiased estimate of
\mu
have smaller variance?