# Probability Product

• Oct 20th 2008, 07:07 PM
lord12
Probability Product
Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables. Show that $P(\max_{i} X_{i} \leq c) = \prod_{i=1}^{n} P(X_{i} \leq c)$.

So use expectation rules?
• Oct 21st 2008, 11:22 AM
lord12
anyone?
• Oct 21st 2008, 12:01 PM
batman
$P(\max_{i} X_{i} \leq c) = P(X_{1} \leq c$ and $X_{2} \leq c$ and $\ldots)$

Now use independence.