# Exponential Distribution
For $X \sim \text{Exp}(\lambda)$,
$
P(X = x) = \lambda e^{-\lambda x}, \quad x \ge 0
$
in which $\lambda$ is the _rate parameter_ of the r.v., $\lambda > 0$.
- Min of multiple exponential r.v.s is Exponential, by summing the rate
parameters.
- Max of multiple i.i.d. Exponential r.v.s
- Consider which one finishes first? (min of the $n$)
- Then by memoryless property, which finishes the second? (min of the $n - 1$)
- And so on.