Skip to main content

TL;DR

A continuous distribution with CDF \( F(x) = 1 - e^{-\lambda x} \) for \( x \geq 0 \), describing inter-arrival times in a Poisson process. It has the memoryless property and mean \( 1/\lambda \).

By Valenke Exam Prep Team·Last updated 2026-06-03

Exponential Distribution

A continuous distribution with CDF \( F(x) = 1 - e^{-\lambda x} \) for \( x \geq 0 \), describing inter-arrival times in a Poisson process. It has the memoryless property and mean \( 1/\lambda \).

Why it matters for interviews

Models waiting times between trades, order arrivals, and events in continuous-time models. The memoryless property makes it the continuous analog of the geometric distribution and is frequently tested in interviews.

Definition and Mathematical Foundation

A continuous distribution with CDF \( F(x) = 1 - e^{-\lambda x} \) for \( x \geq 0 \), describing inter-arrival times in a Poisson process. It has the memoryless property and mean \( 1/\lambda \).

Application in Quantitative Finance

Models waiting times between trades, order arrivals, and events in continuous-time models. The memoryless property makes it the continuous analog of the geometric distribution and is frequently tested in interviews.

Related Terms

Ready to practice for the Quant Trading Interview?

Adaptive practice powered by Item Response Theory targets your weak areas. Start with 3 free sessions.

Start free practice →

Frequently Asked Questions

What is the memoryless property formally?▼
\( P(T > s+t | T > s) = P(T > t) \). The remaining waiting time has the same distribution regardless of how long you have already waited. The exponential is the only continuous distribution with this property.
How does the exponential relate to the minimum of independent exponentials?▼
The minimum of independent exponentials with rates \( \lambda_1, \ldots, \lambda_n \) is exponential with rate \( \sum \lambda_i \). This is used in competing risks models and to analyze the first event among multiple independent processes.
What is the hazard rate?▼
For the exponential, the hazard rate \( \lambda \) is constant -- the instantaneous failure rate does not change with age. This contrasts with the Weibull distribution where hazard can increase or decrease over time.