I suppose you express skepticism that “being randomly sampled” is a meaningful statement. I’m planning an indepth dive into foundations of probability theory in order to clear these kind of confusions and arrive to a propper definition of what “randomness” even means.
For now, consider the two paper picking examples from the post. Even if you don’t exactly understand what randomness is it should be clear that it works different in these examples. In one case you can get any piece of paper from all the papers in the bag. In the other you may not get a piece of paper at all—empty spaces are added as possible outcomes of the experiment.
Likewise consider the third version of paper picking experiment, where the papers are not picked blindly and you always get the paper with number 6, regardless of the bag. Clearly, this situation is quite different from the previous two. In this experiment you have only one possible outcome, where previously there were multiple of them. So we say that in this case there is no randomness.
I suppose you express skepticism that “being randomly sampled” is a meaningful statement. I’m planning an indepth dive into foundations of probability theory in order to clear these kind of confusions and arrive to a propper definition of what “randomness” even means.
For now, consider the two paper picking examples from the post. Even if you don’t exactly understand what randomness is it should be clear that it works different in these examples. In one case you can get any piece of paper from all the papers in the bag. In the other you may not get a piece of paper at all—empty spaces are added as possible outcomes of the experiment.
Likewise consider the third version of paper picking experiment, where the papers are not picked blindly and you always get the paper with number 6, regardless of the bag. Clearly, this situation is quite different from the previous two. In this experiment you have only one possible outcome, where previously there were multiple of them. So we say that in this case there is no randomness.
As saying goes, “constant is a random variable”.
And as another saying goes, “A rose by any other name would smell as sweet”.