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X1, … Xn are i.i.d. random variables, and E(Xi ) = 3β, Var(Xi ) = 3β^2...

X1, … Xn are i.i.d. random variables, and E(Xi ) = 3β, Var(Xi ) = 3β^2 , i = 1 … n, β > 0. Two estimators of β are defined as β̂ 1 = (X̅ /3) β̂ 2 = (n /3n+1 ) X̅

Show that MSE(β̂ 2) < MSE(β̂ 1) for a sample size of n = 3.

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