Let X be a random variable. Suppose we try to use a constant real number â to guess the value of X. Let E(X – â)² be the mean squared error (MSE) of this estimation. (i) By writing X − â = (X − EX) + (E X − î), show that - E(X − â)² = Var(X) + (E X − â)². (ii) Conclude that the MSE is minimized for î = EX and the minimum MSE equals to Var(X).

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