Stastical inference help - derive UMVUE for a discrete distribution

Hi, i am working on some problems for a Statistical Inference course. I am working with a discrete distribution and need to solve for the a) Complete and sufficient theta b) UMVUE c) Cramer-Rao lower bound d) Cauchy-Schwartz Inequality e) asymptotic distribution of the MLE

Some help/tutoring would be great.