Given $N$ random iid variables, $X_1, \ldots, X_N$, with a uniform probability distribution on $[0, 1)$ what is the distribution of $\displaystyle \max_{i = 1 \ldots N}(X_i)$?
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6Shai Covo's post below is an easier way to the right answer. But I wanted to mention that this is a special case of an order statistic. – Nov 25 '10 at 20:03
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Order statistics is better than what I need. – Alexandru Nov 25 '10 at 20:32
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@user856; But the Order Statistics are not Independent. – MSIS Jun 20 '22 at 21:50
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Hint: $\max \lbrace X_1,...,X_N \rbrace \leq x$ if and only if $X_i \leq x$ for all $i=1,...,N$.
Shai Covo
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But I guess after you order them , you destroy their independence, right? Once we know, e.g., the Min, that restricts other values. – MSIS Jun 20 '22 at 21:52