Let X 1 ,X 2 , . . . , X n denote a random sample from a Poisson distribution with parameter , 0 <

Let X₁,X₂, . . . , X_n denote a random sample from a Poisson distribution with parameter θ, 0 < θ < ∞. Let Y =Σⁿ₁ X_i and let L[θ, δ(y)] = [θ − δ(y)]². If we restrict our considerations to decision functions of the form δ(y) = b + y/n, where b does not depend on y, show that R(θ, δ) = b²+θ/n. What decision function of this form yields a uniformly smaller risk than every other decision function of this form? With this solution, say δ, and 0 < θ < ∞, determine maxθ R(θ, δ) if it exists.