True or False:

Please show me the step by step solution of this question:

.. _ 1 1. Suppose that X1,X2, - - - ,Xn 1131' N01,, 0'2) with a a 0, and let X = 5 2X2? be the sample i=1 1 n n _ 1 2(X3- 502 be the sample standard deviation. Answer the following i=1 mean and 8 = Ti'ue/ False questions about estimators for ,u, 0'2, and 0'. (a) X is the UMVUE for p. (b) 6'2 is the UMVUE for 0'2. (0) 6' is an unbiased estimator for 0'. (d) No other estimator for 0'2 has smaller Turarainoe than 6'2. (e) No other estimator for ,u, has smaller varaince than X