Consider a random sample $x_1,x_2,$dots,$x_n$ from a distribution

with probability function:

$f(x,)=(1-{)}^x{I}_{\{0,1,2,\text{d}\text{o}\text{t}\text{s}\}}(x)$

Does a UMVUE for $g()=\frac{1-}{}$ exist? If no$,$ justify your

answer. If yes, find the UMVUE.

b$.$ Does a UMVUE for $$ exit? If no$,$ justify your answer. If yes,

find the UMVUE.

c$.$ Find the MLEs for $$ and $\frac{1}{}$ and compare these estimators

with the corresponding UMVUEs.