# Why are samples always taken from iid random variables?

In most mathematical statistic textbook problems, a question always ask: Given you have $X_1, X_2, \ldots, X_n$ iid from a random sample with pdf:(some pdf). My question is why can't the sample come from one random variable such as $X_1$ since $X_1$ itself is a random variable. Why do you need the sample to come from multiple iid random variables?

-
The samples do come from the same random variable, but the different samples need different names, that is, it makes no sense to say something like "Let $X_1$, $X_1$,$\ldots,$ $X_1$ denote a random sample with pdf $f_X(x)$". –  Dilip Sarwate Oct 3 '11 at 1:17
@Henning: that sure looks like an answer to me... :) –  Ｊ. Ｍ. Oct 3 '11 at 1:28