Q$4)$ Let $x_1,x_2,$dots,$x_n$ be iid random variables with a gamma density defined by :

$f(x$;$)=\frac{1}{{}^2}x{e}^{-\frac{x}{}},x>0.$

a$.$ Compute the method of moment estimator $(hat())$ of $.$

b$.$ Verify that hat$()$ is unbiased estimator for $,$

c$.$ Verify that hat$()$ is consistent estimator for $,$

d$.$ Is hat$()$ minimum variance unbiased estimator for $?$ Why?