Definition of an "Experiment" in Probability One can define the fundamental concepts of probability theory (such as a probability measure, random variable, etc) in a purely axiomatic manner. However, when we teach probability, we start off with the notion of an "experiment", a concept it seems to me which is something akin to pornography: difficult to define, but you tend to know it when you see it.
So I am curious if there is a general definition of an experiment (or if it something really best regarded more as an explanatory construct). To try to define an experiment as a type of function seems difficult to me b/c it would require the notion of a "random function" of some type.
Thanks,
Jack
 A: I like the way it is defined in Mathematical Statistics By Wiebe R. Pestman:
"A probability experiment is an experiment which, when repeated under the same conditions, does not necessarily give the same results"
This is useful as well.
A: One would think that it would be the other way round - everyone understands what it means to roll a die, but the notion of a random variable is far less trivial.
To define an experiment, first define a "generator" - any physical or algorithmic method for producing $N$ numbers, such that $N$ tends to infinity, the numbers produced are distributed according to random variable $X$.
The production of any individual number using a generator is an experiment. 
A: “Experiment is a systematic way of varying all the factors of interest and observing impact of these all factors on the desired output.”
A: While reading Grimmett & Welsh book, I found that an experiment is

Any procedure whose consequences are not predetermined.

This is quite a restrictive definition in my opinion, because it excludes "deterministic" experiments where we can determine the final result 100% precision (because there is actually only one possible result). So to me, it the following definition given by Wikipedia seems more precise:

Any procedure that is infinitely repeatable and whose outcomes are well-defined

This seems fine,  but it doesn't seem tremendously mathematical. So my guess is that the definition above is correct, and that is the definition used to define a sample space, outcomes, events, event space, probability measure, and so on. However, once we've defined all those mathematical structures, we can go back and say: actually, an experiment can easily be represented by a probability space $(\Omega, \Sigma, \mathbb{P})$. This could be seen as a circular definition, but if you use the word "represented" instead of "defined" then you should be fine.
I just wrote an article (which I will extend soon, it's still under construction) in my website SimpleAI

