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4. Let Yi, ½, . . . , Yn be a random sample from some pdf/pmf f(y; θ)·Let W be a point estimator h(y, Y2, . . . , Yn) for θ. The bias of W as a point estimator for θ is defined as W Blase(W) = E(W)- The mean square error of W is defined as MSEe(W) = E(W-0)2 (a) Using properties of expected values, and the definition of variance from PSTAT 120A/B, show that MSEe(W) = Vare(W) + [Biase(W)12 (b) Suppose that f(y:0) is the normal density with mean θ and variance one. The MLE is clearly s n-1 Ση.ly. Find i) an unbiased estimator with greater variance than Y, and ii) a biased estimator with smaller variance than Y

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