In Section 9.3wc emphasized the notion of most efficient estimator by comparing the variance of two unbiased estimators 1 and 2 . However

In Section 9.3wc emphasized the notion of "most efficient estimator" by comparing the variance of two unbiased estimators Θ₁ and Θ₂. However this does not take into account bias in case one or both estimators are not unbiased. Consider the quantity MSE = E(Θ - θ), where MSE denotes mean squared error. The MSE is often used to compare two estimator’s Θ₁ and Θ₂ of 6 when either or both is unbiased because (i) it is intuitively reasonable and (ii) it accounts for bias. Show that MSE can be written MSE = E [Θ – E(Θ)]² + [E(Θ – 6)]² = Var (Θ) + [Bias(Θ)]².