Random Variableshard
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Let X1,X2,,XnX_1, X_2, \ldots, X_n be i.i.d. from a continuous distribution with CDF FF. Let X(1)X(2)X(n)X_{(1)} \le X_{(2)} \le \cdots \le X_{(n)} be the order statistics. What is the distribution of Uk=F(X(k))U_k = F(X_{(k)})?