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

[edit] 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)

[edit] Suggestions

We should:

(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)