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 < $$ F(x)=(1-e^{-x}) $$ and the maximum magnitude is (see < $$F(x)=(1-e^{-x})^n$$ and thus the pdf (just by differentiating) is $$f(x)=n(1-e^{-x})^{n-1}e^{-x}\textrm{.}$$