expo-dist

Exponential Distribution

For $X\sim \text{Exp}(\lambda )$,

$$P(X=x)=\lambda e^{-\lambda x},x\ge 0$$

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.