I am looking for a formal definition of "drawing samples" (or simply of "samples"), can somebody help me?
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I am sure you are referring to random sampling.
The random variables $X_1,X_2,...X_n$ are called a random sample of size $n$ from the population with pdf $f(x)$ if $X_1,X_2,...X_n$ are mutually independent and the marginal pdf of each of them is exactly $f(x)$.