Let X1, n-,X.n be i.i.d. according to a N(0,02) density, and let S2 : 211:1 XE. We are interested in estimating 6 = 02 under the squared error loss L(6, d) = (6 d)2 = (02 d)2 using linear estimator (5mg, 2 032 + b, where 0; and b are constants. Show that (a) The risk of 6011;, is given by 2 R5\" (02) 2 Ear (02 (682 + b)) 2 27111204 + [((m _ \"02 + b]2. (b) The constant estimator 50,20,520 = 0 is inadmissible. Remark: this exercise illustrates the fact the constants are not necessarily admissible