Question: Given the set {U1,.........,Un} of iid uniform (0;T) random variables, we defince Xk = smallk(U1,...........,Un) As the kth smallest element of the set. That is

Given the set {U1,.........,Un} of iid uniform (0;T) random variables, we defince
Xk = smallk(U1,...........,Un)
As the kth "smallest" element of the set. That is , X1 is the minimum element, x2 is the smallest, and so on, up to Xn, which is the maximum element of {U1,......,Un}. That X1,....Xn are known as the order statistics of U1,.........Un
Prove that

X1X (21,... , Tn 0 otherwise.

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