Question: Let X1, ..., Xn be an iid random sample from a population with unknown meant? and a nite variance 02 > 0. In the problem

Let X1, ..., Xn be an iid random sample from a population with unknown meant? and a nite variance 02 > 0. In the problem of estimating 6' E Q = R1 (real numbers) with D = R1 and L(l9,d) = (t9 d)2 (squared error loss), consider a general statistical procedure of the form 5w = Q)? l b, where a and b are general constants. Assume that X3- ~ Bernoulli(9), i.e., P6(X%~ = 1) = 1 P6(X%- = 0) = 9. Assume that the statistician decides to restrict consideration to procedures of the form 6.33, = a}? l b, and want to always yield only decisions in D = [0, l] regardless of the observed value X = (X 1, ..., X\"). Show that the pair (a,b) has to be chosen to satisfy 0 g b S 1 and b g a g l b
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