Let's say, we have $i$ continuous IID random variables $X_1, X_2, \ldots,X_i$ whose domain is $\mathbb R$. This sequence divides the real axis into $i + 1$ intervals. Now, if we have another random $X_j$ who also have the same distribution, is correct that the probability of this $X_j$ falling into these $i+1$ intervals are equal?
(For me, it seems to be intuitively correct since there are no difference between these $X$'s. )