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Question: Let X = min (S, T) and Y= max (S, T) for independent random variables S and T with a common density f. Let Z denote the indicator of the event S <>

a) What is the distribution of Z?

b) Are X and Z independent? Are Y and Z independent? Are (X, Y) and Z independent?

c) How can these conclusions be extended to the order statistics of three of more independent random variables with the same distribution?

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