# 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

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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.

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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.

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My initial reaction is to say that I'm gobsmacked. I'll have to read the article though to understand the context (and his meaning) better. Is this what most statisticians take to be the definition, do you think? Thanks –  Jack Zega Feb 20 '13 at 23:47
@JackZega By no means I'm a statistician. The above tries to convey difference between deterministic experiment versus probability experiments. For example, if you try to measure voltage $V$ through a certain conductor with resistance $R$, you will always end up with the value $IR$ no matter what (this is a deterministic experiment ). One advice, the deeper you go the more hair you lose :) –  jay-sun Feb 20 '13 at 23:55