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As a beginner in probability and statistics I have been confused by usage of the word "sample."

For example in my book on probability we define a sample space $S$, and then we say that $s āˆˆ S$. I had been reading this as "s is a sample in the sample space S," although technically my book has only said that "s is a possible outcome."

Then later in my book, in discussing the famous Birthday problem, it says that when choosing birthdays for $k$ people, we would "sample" the 365 possible birthdays $k$ times.

So a single sample $sāˆˆS$ would be constructed by $k$ acts of sampling. Can it be said that we construct a sample by sampling in this way?

If the answer is yes then that is fine by me, I just wasn't sure if the word could take on two shades of meaning like that.

Or, if $s$ isn't read as "a sample," then what is the best term for it? An "outcome", as my book seems to suggest?

Stephen
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  • Arguably the sample space for $k$ individuals' birthdays is $\{$January $1$, January $2$, $\ldots$, December $31\}^k$ and a sample is a $k$-dimensional element of this $k$-dimensional sample space. So, to me, the two senses you identify are the same ā€“ Henry Jun 25 '17 at 20:38
  • My point is that a single sample ($k$-dimensional element) would then be created by $k$ acts of sampling. So then "sample" (the noun) consists of $k$ "acts of sampling" (the verb). That's what I mean by different senses, although of course they are related. ā€“ Stephen Jun 25 '17 at 21:34

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