Exp

• $\mathrm{rate}$: rate parameter ($\lambda > 0$, controls decay speed; mean = $\frac{1}{\mathrm{rate}}$)

• Formation: the waiting time between events in a Poisson process.
• Origin: naturally arises from memoryless processes where the probability of an event occurring is constant over time.
• Properties: memoryless (past events do not affect future probabilities).
• Applications: time between failures, waiting times in queues, radioactive decay, customer service times.
• Characteristics: always positive, right-skewed with a light (exponential) tail.
• Caution: extreme skewness makes traditional location estimators like $\operatorname{Mean}$ unreliable; robust estimators provide more stable results.