Question: 14. Let (Xn : n 1) be a sequence of random variables which converges in mean square. Show that E ???? [Xn Xm]2

14. Let (Xn : n ≥ 1) be a sequence of random variables which converges in mean square. Show that E

????

[Xn − Xm]2

→0 as m, n →∞.

If E(Xn) = μ and var(Xn) = σ 2 for all n, show that the correlation between Xn and Xm converges to 1 as m, n →∞.

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