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A distribution describing the time between events in a Poisson process; a continuous analogue of the geometric distribution.

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Expected value of maximum of $n$ iid exponential random variables [duplicate]

I was recently playing around with this distribution. Let $Y_n \sim \max_i X_i$ where $X_i \sim \exp(\lambda)$. Then the well-known result $$ f_{Y_n}(y) = \lambda n e^{-\lambda y}(1-e^{-\lambda y})^{n …
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