Question: Let X1, ...,Xn be a random sample from continuous distribution with a cdf F such that F 1 exists. Find (if it exists) the limiting

Let X1, ...,Xn be a random sample from continuous distribution with a cdf F such that F −1 exists. Find (if it exists) the limiting distribution of: (i) Un = nF(X1:n).

(ii) Wn = n[1 − F(Xn:n)]. (iii) Vn = nF(X3:n).

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