6. Let X(1),X(2), . . . ,X(n) be the order statistics of n independent RVs X1,X2, ....

Question:

6. Let X(1),X(2), . . . ,X(n) be the order statistics of n independent RVs X1,X2, . . . ,Xn with common PDF f (x) = 1 if 0 < x < 1, and = 0 otherwise. Show that Y1 = X(1)/X(2), Y2 = X(2)/X(3), . . ., Y(n−1) = X(n−1)/X(n), and Yn = X(n) are independent. Find the PDFs of Y1,Y2, . . . ,Yn.

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