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Consider the following standard definition of mutual independence of (discrete) random variables:

"A set of random variables is mutually independent iff for any finite subset $X_1, ..., X_n$ and any finite set of numbers $a_1, ..., a_n$, the events $\{X_1 \le a_1\}, ..., \{X_n \le a_n\}$ are independent events (as defined above)." Taken from Wikipedia.

My question is: Shouldn't we also have specified that we have to have $n>1$ ? Since otherwise for $n=1$ it is not defined what it mean for just one random variable to be independent. As far as I can see, we need at least two random variables (even if they are the same).

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    Yes, there should be a restriction that $n$ must be at least $2$. See, for example, the last few lines of [my answer](http://math.stackexchange.com/a/267821/15941) to your previous question.2012-12-31
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    @DilipSarwate Ah thanks a lot, I didn't saw the answer until now.2012-12-31
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    Seeing, that since yesterday no one has given a comment or responded, please let me add that although I have two answers and everything, **I still don't know how to formally deduce from the definition of mutual independence that only one variable is always independent**,which is what I want2013-01-01
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    Perhaps you should just believe that the (previous) Wikipedia definition is not quite right and the finite subsets talked of in there should just be restricted to cardinality $2$ or more. Wikipedia is _not_ the final authority on anything. Errors, ambiguities, etc in that electronic tome are not completely unknown and do not necessarily get corrected. The recent edits (by @HagenvonEitzen?) take care of the issue, I believe.2013-01-01
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    @DilipSarwate Agreed. Until Hagens edit come into place (as of present I can't detect any changes), could you please give me a reference to a book where I can find a proper definition of mutual independence ?2013-01-02

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