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If you have a set of numbers of $n$ numbers: $D = \left\{x_1, x_2, x_3, \ldots, x_n\right\}$.

I am trying to determine its probability space, but I don't understand how to get this. To see if $x_i$ in $D$ being repeated, you need to compare it to the other values of $D$. But I don't know how to go further.

Can anyone help please?

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Set by definition has distinct objects. –  jay-sun Mar 6 '13 at 0:38
    
What distribution are the $x_i$ drawn from? It seems likely that is is from $[1,m]$ uniformly with replacement. Is that so? –  Ross Millikan Mar 6 '13 at 0:39
    
I think it's just Z (set of integers) with uniform probability. –  omega Mar 6 '13 at 0:40
    
@omega: there is no uniform distribution over $\mathbb Z$. There is one over an interval of $\mathbb R$ but the probability of a match is then zero for any finite set. –  Ross Millikan Mar 6 '13 at 1:29
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