Let $\displaystyle X_{1}, X_{2}, \ldots, X_{n} $ be independent random variables. Show that $\displaystyle P(\max_{i} X_{i} \leq c) = \prod_{i=1}^{n} P(X_{i} \leq c) $. So use expectation rules?
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$\displaystyle P(\max_{i} X_{i} \leq c) = P(X_{1} \leq c$ and $\displaystyle X_{2} \leq c $ and $\displaystyle \ldots)$ Now use independence.
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