Please answer all parts as best as you can :)

(50) Let Y be a continuous random variable with pdf fy (y; 0) = -e-410, y >0 (a) (10) Prove that E(Y) = 0 and Var(Y) = 02 (pleaes include the details). (b) (5) Let Y1, Y2, ..., Yn be a random sample from fy(y;0). Find the MLE for 0. (c) (5) Show that T is an unbiased estimator of 0, where T= = (Y1 + Y2 + ... + Yn). (d) (10) Show that T is a consistent estimator of 0. (e) (5) Show that T is a sufficient statistic for 0. (f) (10) Find the Cramer-Rao lower bound for the variance of unbiased estimators of 0 (g) (5) Show that T is the MVUE of 0