(6+6+6+6=24 pts ) Let X 1
​
,X 2
​
,…,X n
​
be a random sample from the distribution with pdf f(x;θ)=e θ−x
I (θ,[infinity])
​
(x) (a) Show that S=X (1)
​
is sufficient for θ. (b) Find the pdf for X (1)
​
. (c) Show that S=X (1)
​
is a complete statistic for estimating θ. (d) Find the UMVUE for θ.