Question: Let X1, X2, . . . , Xn be independent identically distributed random variables with cumulative distribution function F(x)= 1/(1+e -x ) , xR. Find

Let X1, X2, . . . , Xn be independent identically distributed random variables with cumulative distribution

function

F(x)= 1/(1+e-x) , xR.

Find the distribution of X1:n + log n, where X1:n = X(1) = min{X1, . . . , Xn}, and compute its limit as n .

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