1. ## maximum likelihood estimate

Suppose X is a single observation from normal (μ,1). find 95% confidence interval for μ?
(use maximum likelihood estimate)

2. you can plug into the usual formula with n=1 and X=sample mean
or solve for moo....

$.95=P(-1.96
and you need not make it symmetric, but that's all that people are doing these days...

(X-1.96,X+1.96) is the answer in that case.