Suppose that iid Y1,..., Yn" fy(y; 0) = = ye-y/0 604 , Y > 0 FUN FACTS E(Y) = 40 V(Y) = 402 1) Show that the MLE of theta is Y 4 2) Verify that the MLE is an unbiased estimator for theta 3) Verify that the Method of Moment's Estimator (MOME) is the same as the MLE. 4) Use the factorization theorem to show that n Y; i=1 is a sufficient statistic for theta. Explain why the MLE is a Minimum Variance Unbiased Estimator (MVUE) for theta.