If $2n$ samples are generated in the following way:
- Draw $U_i\sim Unif[0,1]$ i.i.d. for $i=1,...,n$
- Define $\tilde U_i := 1 - U_i$ for $i=1,...,n$
If I would now draw a random sample $X$ among these $2n$ samples, why wouldn't its distribution be a mixture of $Unif$ and $1-Unif$ and thus just $X \sim Unif$?
I'm not sure if it is clear what I am trying to ask, so let me give an analogy: Everyday a tree of random height $U_i$ is grown together with a second tree of height $1-U_i$. Now what is the CDF of the height of trees?