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  1. Is it right that elements of both samples and sample space are called `outcomes'?
  2. Is it right that a sample is an array of outcomes?
  3. What is an outcome of an experiment: a sample, event or outcome?
  4. I do not understand why (1,1) is an outcome but "sum of two dice is 7" is an event. Why I cannot say that "sum of dice is 7" is an outcome of my experiment?

I guess that sample is something used by statisticians whereas event and outcome is from the vocabulary of probabilists but not sure.

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  • $\begingroup$ 1. Sample is just something you get from experiment. Sample space is all possible samples you can get by repeating the experiment infinitely. $\endgroup$
    – SmallChess
    May 14 '17 at 13:12
  • $\begingroup$ Outcome is something I get from the experiment. I ask to contrast the terms. Otherwise, they seem identical to me. $\endgroup$
    – Val
    May 14 '17 at 13:16
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    $\begingroup$ Please start by consulting a textbook or a standard reference like Wikipedia. $\endgroup$
    – whuber
    May 14 '17 at 14:54
  • $\begingroup$ Which textbook? I clearly ask because those textbooks and Wikipedia confuse me. Let somebody who has figured out have a chance to clear things up. Moreover, I was advised to post here from the chat. They advised me to post here instead of consulting these confusing sources. $\endgroup$
    – Val
    May 14 '17 at 15:37
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1-Yes, but the sample space collects a larger number of possible outcomes (all of them) as the sample (some of them), given that the sample is a subset of the sample space.

2-An array is a data structure that contains elements (integers, words); it is used in computer programming.

3-The outcome of an experiment is an event. In particular, the Sample Space contains all simple events (i.e. all possible outcomes). The event is used to 'formalize' all outcomes of an experiment and make the solutions and notation less tedious.

4-As I said in 3, since the event is a formalization of the outcome, both words are often interchanged and used as synonyms to make the theory text less heavy on the reader. In this case, I think the word outcome is used for (1,1) since it is a simple event. Unfortunately, use of mathematical jargon is often inconsistent across different texts, and thus an outcome might mean something different in some books than how I defined it above.

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    $\begingroup$ In my experience, (good) textbooks make a consistent and clear distinction between outcomes and events. In particular, they do not characterize events as "outcome of an experiment" (which is vague, anyway). Please visit stats.stackexchange.com/questions/143459/… as well as the links provided in the answers there. $\endgroup$
    – whuber
    May 15 '17 at 17:46
  • $\begingroup$ I know what array is. Sample also contains elements, the measurement outcomes. That is why I ask if it is an array (or may be set?) of outcomes. $\endgroup$
    – Val
    May 15 '17 at 19:31

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