Let X 1 ,X 2 , . . . , X n denote a random sample from a distribution that is N(, ), 0 <

Let X₁,X₂, . . . , X_n denote a random sample from a distribution that is N(μ, θ), 0 < θ < ∞, where μ is unknown. Let Y = Σⁿ₁ (X_i − ‾X)²/n and let L[θ, δ(y)] = [θ−δ(y)]². If we consider decision functions of the form δ(y) = by, where b does not depend upon y, show that R(θ, δ) = (θ²/n²) [(n²−1)b²−2n(n−1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form.