Question: Let X1, ...,Xn be a random sample from a logistic distribution with a cdf F(x) = 1/(1 + ex), and let Vn = Xn:n. Then

Let X1, ...,Xn be a random sample from a logistic distribution with a cdf F(x) =

1/(1 + e−x), and let Vn = Xn:n. Then Vn P

→∞, but Vn − log n has a proper limiting distribution. Find limn→∞P{Vn − log n ≤ 0} and limn→∞P{|Vn − log n| ≤ 1}.

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