# Talk:Sample space

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"Any discussion of the probabilities of events begins with a precise definition of all the possible events. This is called the sample space"

The above is bad writing; if I weren't so rushed I'd replace it with something that makes sense. Events are subsets of a sample space; outcomes are members of a sample space; I usually point out things like this when grading undergraduates' homework assignments. I a forum like this I have far less patience. -- Mike Hardy

## Connection between probability and statistics

It would be useful to include a discussion of the relationship between sample space and sample from a population. I'm not sure enough on this point to write anything on the article myself, but for discussion I'll suggest the following:

In statistics the result of conducting an experiment is viewed as a sample from a population. In this case the sample space consists of all possible ordered sequences of members of the population (all possible samples). A sequence of random variables is then defined on the sample space, which give the observations x_1,x_2,...,x_n.

This is my idea of how this connection is formalised, anyone got anything to add (or take away!) ? --SgtThroat 11:29, 15 November 2005 (UTC)

## Suggestions

We should:

What? this don't make since! <3 Falon(:

(a) Incorporate the articles on "Sample Space" and "probability space" into the article on "probability theory";

(b) Be careful to distinguish between "Probability Space" and "Sample Space"; the distinction between them is indeed both mathematically and conceptually important; confusing the two is akin to the following: not distinguishing between the domain and range of a function; not distinguishing between the image under a funtion and its preimage.

(c) Improve the article on "probability theory".

Note corrections to the entry on probability space that have already been done.

Please, as mathematicians, let us be precise.

MathStatWoman 19:42, 22 December 2005 (UTC)

(D) We should have a link to some website or place where students can get instant solution for their questions on probability and sample space

## Questions

(a) Where does "universal sample space" come from? I have not seen this term before, and I would love a reference. Usually this sample space is simply called "the sample space". Other sample spaces (such as random variable codomains) get no special distinction, if the word "the" can be called a special distinction.

(b) What are "subsets of interest" and why should they correspond to some sub-σ-algebra?

## My opinion

A sample space must be the sample itself since all the sample points constitute a space, the sample or the sample space. The examples in the article here are actually "measurability" or scale space for the relevant experiments. They are not the samples of the experiments. ----Yuanfangdelang (talk) 16:14, 21 October 2010 (UTC)

With the new content I've added and the organization, grammar, and clarity work I've done, I'm re-rating this article as C-class; it appears comparable to the examples given on the assessment page. Hope others agree! -Bryanrutherford0 (talk) 00:42, 18 July 2013 (UTC)

## visual example of a sample space

Sample spaces relating to the Monty Hall Problem

I am interested to post a graphic of a visual example of a sample space (to be incorporated into this article), so as to provide a reference by which novice learners can more quickly grasp the meaning of the term. I attempted to advance a dialog on this point over at Talk:Monty Hall problem but ran into a buzzsaw of entrenched editors there who naysayed and obtusely opposed that discussion. Suffice it to say, I do not want a repeat of that here; so does anyone have any suggestions or thoughts about visual examples of "sample space"? In my failed effort to advance the dialog at MHP, I posted a diagram, but I do not think that diagram is good enough to serve its purpose - and I need to encourage a dialog. Tweedledee2011 (talk) 01:31, 2 January 2014 (UTC)

"the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment" The result of the first choice is "Monty opens a door with a goat, and offers to switch.". The result of the second choice is "Monty opens a door with a goat or with car". The diagram does not reflect this. Paradoctor (talk) 15:02, 3 January 2014 (UTC)
WP:BURDEN: "The burden of evidence lies with the editor who adds or restores material". If you want to keep editing here, you need to familiarize yourself with the rules. Paradoctor (talk) 00:28, 4 January 2014 (UTC)
Tweedledee2011 – what are you after? You talk about "sample space" without considering what "sample space" exhibits.
It seems to me that you do not distinguish "sample space" (all possible outcomes) and the probability of any outcome to come true. What are you after?
Your diagram first shows first 3 doors, and then in the following second part thereafter shows the remaining two still closed doors after the host has intentionally shown one single goat: The still closed door that was first selected by the guest, and the still closed host's door that he offeres to switch on. And you conclude the chances staying:switching are 50/50. False! Chances are 1:2.
Please read vos Savant: Your diagram could first show as well one million doors, and then the following second part of your diagram still shows the two remaining closed doors – after the guest selected ("guessed" is not the correct word) one door (with chance of one in a million), and threafter the host showed 999'998 goats, then the sample space of the two remaining closed doors is exactly what you depict: The still closed door first selected by the guest (with a chance of 1 in a million) and the door offered to switch on with a chance of 0,999999. Even for this variant your second part shows just the "sample space" and nothing more. We cannot read the "chance" of any outcome just by denominating the "sample space" of a random trial, without showing the chances of any non random trial. So what are you 'after? Gerhardvalentin (talk) 00:11, 4 January 2014 (UTC)
Gerhard - I'm trying to illustrate what the player's available sample space visually looks like before the just 2nd choice. That's the purpose of this discussion. Are you going to help with that or not? Tweedledee2011 (talk) 01:12, 4 January 2014 (UTC)
This is the talk page of the article sample space, not the Monty Hall problem. Please state what changes you want to be made to this article. Paradoctor (talk) 01:29, 4 January 2014 (UTC)
Changes I seek:
1) I want to include a block diagram to illustrate a simple sample space into this article.
2) Since MHP is a well known probability problem, a block diagram which illustrates a simple sample space for that, makes sense here.
Tweedledee2011 (talk) 02:12, 4 January 2014 (UTC)
Samples spaces are sets, I don't see how a block diagram is useful here. Graphical representations of small finite sets are usually Venn diagrams.
Since sample spaces, if discussed beyond a simple definition at all, will generally be illustrated in textbooks on probability theory and statistics, illustrations used there clearly carry more WP:WEIGHT than a self-made illustration for a basically unrelated topic. Should no such illustrations exist, then that would be an argument against using an illustration here.
Since we're discussing at MHP, further discussion here should wait until the matter there is settled. Paradoctor (talk) 03:25, 4 January 2014 (UTC)