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Let $X_1$ and $X_2$ be independent random variables with c.d.f. $F_{X_i}(x_i)$, $i = 1,2$. Find the c.d.f. of $U = \min(X_1, X_2)$ and $V = \max(X_1, X_2)$.

I'm stuck at this exercise for a while and even searching for similar questions I didn't find out exactly what I'm supposed to do. Those min and max burn my brain already.

Thanks in advance.

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    that is indeed the answer.2012-11-20

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A start: Let random variable $S$ be the maximum of $X_1$ and $X_2$. Then $S\le s$ iff both $X_1$ and $X_2$ are $\le s$. By independence, this probability is $\Pr(X_1\le s)\Pr(X_2\le s)$. Thus $F_S(s)=\dots$.

Now you can do tackle the minimum. It is somewhat harder, but goes along similar lines.

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    Works like a charm. Thanks :)2012-11-19