In the context of ordered statistics, each of Y(1),Y(2),...,Y(n) a single observation or distributions that are I.I.D? In statistics one aspect of the I.I.D. concept that bothers is when I think about it in the context of ordered statistics. As most of you already know, $Y_1,Y_2,Y_3,...,Y_n$ are I.I.D. when the parameters are the same. 
Now, here are two things I'm confused about. 


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*In the context of ordered statistics, each of $Y_{(1)},Y_{(2)},...,Y_{(n)}$ a single observation or distributions that are I.I.D?

*If they are distributions, how in the world is it possible to order distributions from the least to greatest??


Toss two coins.  Let $Y_i=1$ if the i-th coin is a head and $Y_i=0$ if it is a tail.
Then we have $\{Y_1, Y_2\}$, which are two independent and identically distributed Bernoulli random variables.
So what does the distribution of $\{Y_{(1)}, Y_{(2)}\}$ look like?
$$\begin{array}{l|llll:l} ~ & TT & HT & TH & HH
\\ \hline Y_1 & 0 & 1 & 0 & 1
\\ Y_2 & 0 & 0 & 1 & 1
\\ \hdashline Y_{(1)} & 0 & 0 & 0 & 1 & \min\{Y_1, Y_2\}
\\ Y_{(2)} & 0 & 1 & 1 & 1 & \max\{Y_1, Y_2\}
\end{array}$$
Clearly they are is not identical nor independent.   (If you know that the largest is $0$ then the smallest is certainly also $0$.)
