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?