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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- Oct 20th 2008, 06:07 PMlord12Probability Product
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? - Oct 21st 2008, 10:22 AMlord12
anyone?

- Oct 21st 2008, 11:01 AMbatman
$\displaystyle P(\max_{i} X_{i} \leq c) = P(X_{1} \leq c$ and $\displaystyle X_{2} \leq c $ and $\displaystyle \ldots)$

Now use independence.