2
$\begingroup$

My book defined 'outcome space', but then went ahead and used the term 'sample space' without definition.

The collection of all possible outcomes [of a random experiment] is called the outcome space.

In an example, my book said the following:

A fair six-sided die is rolled six times. If the face numbered $k$ is the outcome on roll $k$ for $k=1, 2, ..., 6$, we say that a match has occurred. The experient is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The sample space is {success, failure}. Let A = {success}...

Are these two words synonymous? If not, what are their meanings? Also, is there some reason why the sample/outcome space is called a space as opposed to a set?

EDIT:

The book is Probability and Statistical Inference by Hogg, Tanis, Zimmerman, 9th edition, Global edition. ISBN-10:1-292-06235-5

The first quote is from page 10. The second is on page 13.

$\endgroup$
  • $\begingroup$ Can you link to the book you are referring to? $\endgroup$ – Antoni Parellada May 15 '17 at 23:35
  • $\begingroup$ @AntoniParellada I edited the question with that information. $\endgroup$ – Ovi May 16 '17 at 0:02
  • $\begingroup$ I found this thread on the topic. $\endgroup$ – Antoni Parellada May 16 '17 at 0:39
  • $\begingroup$ Regarding the thread on physicsforums.com mentioned in the comment above by @AntoniParellada: I disagree with response #2 there by StatsTiger. A brief summary of StatsTiger's interpretation is e.g., for rolling a pair of dice, the outcome space is $\{(1,1), (1,2), \ldots, (6,6)\}$ where as the sample space is still $\{1, 2, \ldots, 6\}$ - this is incorrect. The other responses on that thread are fine. $\endgroup$ – Just_to_Answer May 16 '17 at 3:21
2
$\begingroup$

They are synonymous - both define the possible samples you can get from your experiment. Why are they called spaces? In mathematics, a "space" is not just a set, but implies there is some relationship among the members of the set.

For example $\{A,B,C\}$ is just a set of three objects, but if they represent an alphabet, we can call it a 'lexical space' or something like that.

Here's an interesting paper discussing spaces vs sets.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.