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In a textbook of mine I detected the follow definition of a random sample:

"Every possible sample of size n has the same probability of being selected"

However, I also already saw some definitions that are formulated like the following:

"Every unit has the same probability of being selected"

Therefore, I wanted to know, whether these two definitions are equivalent.

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  • The first definition needs first a definition of "sample" to make sense. – Xi'an Jan 13 '23 at 15:22
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    The second is not a correct definition. For instance, consider samples of size $2$ from the set ${0,1,2,3}$ and suppose the samples ${0,1},$ and ${2,3}$ have equal chances of $1/2$ to be your sample. Each unit has probability $1/2$ of being selected, but there is no chance that $1$ and $2$ occur in the same sample. – whuber Jan 13 '23 at 16:32

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