Continuous probability distribution
Exponential distribution
X ~ Exponential(λ)
The waiting time until the next event in a Poisson process. It is "memoryless": the probability of waiting an extra minute does not depend on how long you have already waited.
Explore it interactivelyKey facts
- Notation
- X ~ Exponential(λ)
- Type
- continuous
- Parameters
- λ — rate parameter (λ > 0)
- Support
- [0, ∞)
- f(x) = λ e^(−λx), for x ≥ 0
- Mean
- 1 / λ
- Variance
- 1 / λ²
When to use it
- Time between customer arrivals
- Lifetime of a component
- Time until the next failure
- Gap between radioactive decays
Related distributions
Frequently asked questions
What is the Exponential distribution?
The waiting time until the next event in a Poisson process. It is "memoryless": the probability of waiting an extra minute does not depend on how long you have already waited.
What are the mean and variance of the Exponential distribution?
For X ~ Exponential(λ), the mean is 1 / λ and the variance is 1 / λ².
When is the Exponential distribution used?
It is commonly used for: Time between customer arrivals; Lifetime of a component; Time until the next failure; Gap between radioactive decays.