Exponential distribution - maximum earthquake magnitude Suppose $n$ earthquakes occur, and suppose the magnitude of earthquakes are independent and have an exponential distribution with mean $1$. What is the pdf of the maximum earthquake magnitude?

The cdf of single magnitute is (see http://en.wikipedia.org/wiki/Exponential_distribution) 
$$
F(x)=(1-e^{-x})
$$ and
the maximum magnitude is (see http://www.math.ucsd.edu/~gptesler/283/slides/longrep_f13-handout.pdf) $$F(x)=(1-e^{-x})^n$$ and thus the pdf (just by differentiating) is $$f(x)=n(1-e^{-x})^{n-1}e^{-x}\textrm{.}$$
