a. Use Tchebychevs inequality to show that if E(X n ) = n and var(X n

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a. Use Tchebychev’s inequality to show that if E(Xn) = µn and var(Xn) = σ2n < ∞, then (Xn – µn) = Opn).

b. Suppose that Y1,..., Yn are independent with E(Yi) = µ and var(Yi) = σ2 for i = 1,...,n. Let Y̅n = (∑i Yi)/n. Apply part (a) to show that Y̅n – µ = Op(n–1/2).

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