I'm reading a book on probability theory and they say that an experiment is
Any procedure that has not got a pre-determined outcome
In the Wikipedia page they, instead, that an experiment should:
- be infinitely repeatable
- have well-defined set of possible outcomes
Now, I really don't see why it has to be infinitely repeatable. I mean, it makes sense only for frequentist probability right? Surely not for bayesian one.
Anyway, my question is: then what is NOT an experiment? what are some examples of procedures that are not experiments?
My Solution
My idea is that the following are experiments:
- Tossing a fair coin, and looking at which side is facing upward after landing.
- Tossing a fair dice, and looking at which side is facing upward after landing.
- Picking up a numbered ball from within a box (where balls are placed randomly and the picking up mechanism is fair) and looking at the number of the ball.
However, I can't quite make up any sensible example of something that is NOT an experiment. For instance, I think that also the following is an experiment:
- Tossing a non-fair coin that always lands on HEAD and looking at the side facing upwards.
because even though the coin is biased, it is infinitely repeatable and has well-defined set of possible outcomes.
What are some examples of non-experiments?
Best Answer
An example of a procedure that is not infintely repeatable is drawing a marble from an urn with a finite number of red and blue marbles in it, without replacement, and observing the color.
It has a well-defined set of possible outcomes (i.e. $\{\text{Blue},\text{Red}\}$), but it is not infinitely repeatable. Eventually we will run out of marbles.