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Problem 4. (Extremes) Let (X,) be iid standard normal random variables. Let Mn = maxisign Xn 1. (Mill's inequality) show that for > > 0, 12 + 1 2. Show that for any 0 E R we have P(Xi > r + (0/x)) / P(X, > x) - e-0 3. Show that if we let by solve P(X1 > bn) = _ then P(bn ( Mn - br )