Definition: Consider a set of random variables X1,X2,...,Xn, the "order statistics" are the same random variables arranged in increasing (actually nondecreasing) order, i.e. X(1)<X(2)<...<X(n) After reading a few more paragraphs, I immediately ran into deep confusion because I cannot make any sense of it... My confusions: 1. X1,X2,...,Xn are random VARIABLES (not constants), so you don't know exactly what the outcome will be. For example the set of possible values of each Xi may be the interval [0,1]. How can you possibly order something that you can't even tell the exact value? (this is like saying [0,1] is less than [0,1]) This makes no intuitive sense to me... 2. "Distributions of Xi's and X(i)'s are NOT the same." How can this be true? They are just the SAME random variables ordered in a different way, how can they distributions possibly be different? I can't make sense of this either... 3. "If the random variables X1,X2,...,Xn are continuous, the equality signs in X(1)<X(2)<...<X(n) can be ignored." Now...I can't see WHY? Could someone please explain? I have read the related material in 2 different textbooks, but they are saying pretty much the same thing and do not clear my doubts at all. Any help would be appreciated!