Exponential distribution: setup, memorylessness, use cases.

medium

Answer

$X ~ Exp(λ): time between events in a Poisson process.$
$PDF: f(x) = λ * e^(-λx) for x \geq 0.$
$\operatorname{Var}(X)\; = \;1 / {\lambda}^{2}$
$P(X\; > \;s + t\; \mid \;X\; > \;s)\; = \;P(X\; > \;t)$
$Uses: waiting times (until next call, next failure), radioactive decay, survival analysis (constant hazard rate).$

Check yourself — multiple choice

E = λ
Waiting times in Poisson process; f(x) = λe^(-λx); E = 1/λ, $\operatorname{Var}\; = \;1 / {\lambda}^{2}$ ; memoryless
Discrete only
Var = λ

Exponential: E = 1/λ, memoryless, waiting times.

#distributions#probability

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