Show that the algorithm in Sec. 8.2.1 for generating the ith order statistic is valid when F is strictly increasing. [Hint: Use the fact that if U1, U2, …, Un are IID U(0, 1), then U(i) ~ beta(i, n – i + 1).] Verify directly that for i = 1 and i = n it is valid to let V = 1 – U1/n and V = U1/n, respectively.
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